transportation planners

Abstract: Traffic forecasting requires modeling complex temporal dynamics and the spatial dependencies imposed by road topology. Supervised graph-based models achieve strong performance, but are often trained for a particular dataset and sensor graph, making deployment to new or evolving networks costly. Prior-Data Fitted Networks (PFNs) offer a zero-shot alternative by learning in-context inference from synthetic task priors, which provide an explicit mechanism for encoding domain-specific assumptions. Existing forecasting PFNs, however, do not explicitly represent the graph-structured dependencies governing traffic dynamics. To combine graph-aware traffic modeling with zero-shot adaptation, we introduce the Graph-Aware Spatiotemporal Prior-Data Fitted Network (GAS-PFN). GAS-PFN incorporates sampled road topology into its synthetic task prior through random-walk diffusion, teaching the model to learn graph-coupled dynamics during pretraining. Its co-designed inference architecture uses two mask-conditioned passes through a shared Transformer backbone to separately model sensor-specific temporal dynamics and spatiotemporal interactions among neighboring sensors before integrating their representations for prediction. This design enables GAS-PFN to use target-network structure and context without parameter updates. Across six benchmarks at the 90-minute horizon, GAS-PFN reduces MSE by 34.0% on average relative to TimePFN, its closest PFN-based predecessor. It also reduces MSE by 27.7% on average relative to four recent industry-developed general-purpose zero-shot forecasters. In this comparison, all models receive 90 minutes of contiguous recent history, and any additional context is drawn from each dataset's chronological training split. These results indicate that aligning PFN priors and inference architectures with graph structure improves in-context learning for zero-shot traffic forecasting.

Abstract: Self-supervised learning has emerged as a powerful paradigm for Path Representation Learning (PRL) in road networks. PRL aims to learn informative representations of paths traversed by moving objects, such as vehicles, where each path consists of a sequence of connected road segments. These representations are essential for various downstream tasks, including travel-time estimation and path ranking. However, existing methods often suffer from ineffective view generation and inefficient training procedures due to their reliance on heuristic augmentations and computationally intensive contrastive learning. To address these issues, we propose AutoPRL, an effective and efficient self-supervised PRL framework that integrates three key components. The Automatic Data Augmentation (AutoDA) module employs variational autoencoders to generate semantically meaningful and diverse feature-level path views by modeling each topology-aware node embedding with a Gaussian latent distribution, thereby mitigating information loss and enhancing representation quality. Second, the Cross-View Decoupled Contrastive (CVDC) learning mechanism improves training efficiency by disentangling the optimization of positive and negative pairs across node- and path-level views, enabling more stable contrastive learning. Third, an Adaptive Co-Training (ACT) module dynamically adjusts uncertainty-based loss weights to balance multiple objectives, ensuring efficient and scalable training. Extensive experiments on three real-world datasets demonstrate that AutoPRL achieves strong and consistent performance in both effectiveness and efficiency across multiple downstream tasks.

Abstract: Spatio-temporal graph neural networks combine a node's history with information from graph neighbors. The central question is whether graph neighbors provide predictive information beyond each node's own history. Forecast accuracy depends on both the choice of neighbors and the way graph messages enter the temporal model. We study these choices as graph construction and graph exposure on U.S. state unemployment, traffic speed, and electricity demand. Our diagnostic design uses two comparisons: varying exposure while holding the domain graph fixed, and varying construction while holding late gated integration fixed. A GRU using only each node's own history and randomized graph controls help assess what the graph contributes. Under a common change forecasting protocol, the same domain graph can improve or worsen error relative to the GRU across integration designs. Late integration alone is insufficient, while adding a fusion gate yields lower mean error in all three tasks. With late gated integration fixed, a graph based on residual correlations has the lowest mean error among the tested graphs, although randomized graphs perform similarly on unemployment. The findings support evaluating graph construction and integration together, with conclusions tied to the comparisons actually performed.

Abstract: We consider the problem of setting tolls on a subset of the arcs of a congested network so as to maximize the revenue of a network authority, anticipating that users route according to a Wardrop equilibrium. This problem is naturally cast as a bilevel program in which the leader sets tolls while the followers respond by choosing an equilibrium routing. We focus on the important special case of separable affine arc cost functions. Under this assumption, Wardrop equilibria admit Beckmann's convex characterization, from which we derive three new single-level reformulations of the bilevel problem, exploiting both Beckmann's formulation and its dual: an arc-based formulation, which we solve exactly, and two path-based formulations, solved by column-and-constraint generation. Beyond the reformulations, we further derive from Beckmann's potential an upper bound on the optimal revenue that can be used to certify optimality gaps across all formulations. An extensive computational study on instances derived from the Sioux Falls and Eastern Massachusetts networks compares our formulations with the recent mixed-integer nonlinear formulation of Beck, Labbé and Schmidt. The arc-based formulation solves substantially more instances to proven optimality (within a time limit of 1800 s) than this formulation and, unlike it, returns a feasible solution on every instance. It remains effective on the largest, 74-node network, on which the formulation of Beck et al. solves none. The magnitude of the upper bounds on the tolls proves to be a major driver of tractability: the genuinely hard core of the benchmark emerges once the regulatory cap on tolls is removed. The two path-based formulations, used as heuristics, return a solution within one percent of the optimum on every instance whose optimal value is known, often in seconds where exact formulations reach the time limit.

Abstract: Traffic forecasting models based on spectral graph convolution offer an interpretable account of how information is mixed between sensors, but they rely on an eigendecomposition of the graph Laplacian. It costs cubic time, is fixed by the road network, and provides a symmetric operator that cannot represent the directed propagation of traffic congestion. Attention-based spatio-temporal transformers remove these limitations but generate a dense sensor-by-sensor attention map at each layer and time step, so memory, rather than accuracy, becomes the binding constraint on large networks. We introduce the spectral adaptive graph transformer, whose spatial operator is learned rather than derived from the Laplacian, directed rather than symmetric, and conditioned on the current traffic state rather than a static state, at a cost linear in the number of sensors. A sparse road graph diffusion branch provides the strictly local propagation that a low-rank operator cannot express, and a zero-initialized gate learns the balance between the two. Before spatial mixing, a unit-mean-gain frequency-bin attention module reweights each sensor's short-term periodicities according to its identity and current context. Across six public benchmarks spanning 170 to 1843 sensors, evaluated over three random seeds, the proposed model attains the lowest error of any single end-to-end model on one benchmark and remains competitive with the strongest current attention models on the others, while using about a quarter of their memory and training about twice as fast.

Abstract: We study the replacement paths problem in unweighted directed graphs with $n$ vertices and $m$ edges under one or two edge failures. We give simpler and faster algorithms for both settings. Both algorithms are based on a new technique, which we call \emph{modulo-layer hitting sets}. For the single-failure setting, we obtain a simple deterministic combinatorial algorithm running in $O(m\sqrt{n})$ time, which is nearly optimal under the combinatorial Boolean Matrix Multiplication (BMM) conjecture. In addition to removing the logarithmic overhead of the deterministic $\tilde{O}(m\sqrt{n})$-time algorithm of Alon, Chechik, and Cohen~[ICALP'19], our algorithm admits a much simpler implementation and analysis. For the dual-failure setting, we obtain a randomized combinatorial algorithm running in $\tilde{O}(n^{3-1/4})$ time. This improves upon the previous $\tilde{O}(n^{3-1/18})$-time combinatorial algorithm of Chechik and Zhang~[ICALP'24].

Abstract: Controlled experiments are essential for advancing transportation research, yet designing eXtended Reality (XR) environments for behavioural studies remains technically demanding and inaccessible to many domain researchers. Current workflows require proficiency in game engines such as Unity or Unreal Engine, imposing significant barriers to rapid scenario prototyping and iterative experiment design. This paper presents XARA, a novel system that integrates a dual large language model (LLM) architecture with an immersive XR environment to enable voice driven experiment generation for transportation research. XARA employs a pipeline in which spoken natural language commands are first transcribed and then interpreted into structured commands that manipulate a Unity based XR scene in real time. The system supports object creation, spatial manipulation, animation control, and scene persistence through a modular architecture. By lowering the technical threshold for XR experiment creation, XARA enables transportation researchers to rapidly prototype driving, pedestrian, and urban design scenarios using intuitive voice commands and hand gestures within an immersive 3D environment. This paper describes the system architecture, the voice to command pipeline, and discusses potential applications across behavioural travel experiments, safety studies, human factors research, and policy testing.

Abstract: Computing the top-$k$ \textit{simple} shortest paths between two vertices of a graph, i.e., solving the P-KSSP problem, is a fundamental primitive in graph analytics. In modern scenarios, however, queries are rarely one-shot: parameters change as applications adapt their information needs, and recomputing a solution from scratch at every request quickly becomes a bottleneck. We study P-KSSP in a dynamic setting, focusing on changes of the parameter $k$: given a top-$k$ solution for a pair of vertices and a new value $k'$, the goal is to compute a top-$k'$ solution reusing the previously computed paths. Our approach rests on the \textit{pseudo-tree}, a compact representation of a collection of simple $s$--$t$ paths: we show that building it from an arbitrary, unstructured solution amounts to trie construction, and give two constructions running in time linear in the size of the collection. On top of it, we design UPD, a dynamic algorithm that updates a solution upon a change of $k$; we prove its correctness, analyze its complexity, and show that it is a general, solver-agnostic scheme, which starts from the paths alone, is parametric in the routine that generates candidate paths and combinable with known preprocessing techniques, as well as with an online pruning rule that we formalize. While a worst-case update is asymptotically comparable to recomputing from scratch, an extensive experimental evaluation shows that a variant of UPD is the fastest method in the large majority of tested configurations, often by a wide margin (with speedups over recomputation that grow with $k$ and $k'$ and exceed $60\times$), yielding a practical recipe for the configuration to deploy.

Abstract: Recent advances in mean-field games and its multi-population variants enable large-scale heterogeneous multi-agent systems to be modeled through representative agents and their associated mean-field distributions. However, existing approaches do not explicitly account for uncertainty in the behavior of other populations. To this end, we introduce a new paradigm: risk-averse multi-population mean-field games, where each population optimizes a worst-case expected reward over dynamically feasible ambiguity sets of mean-field flows of a subset of the other populations. Employing an occupation-measure formulation along with tools from set-valued analysis, we establish, under mild assumptions, several theoretical properties of the multi-population game, including the geometric properties of the ambiguity sets and the existence of a novel risk-averse multi-population mean-field equilibrium. Further, we derive contractivity results of the fixed-point operator under entropy regularization and show that it can be utilized to learn the equilibrium. Finally, we propose a risk-averse fictitious-play scheme and show that exploitability decays to zero, despite the additional nonlinearity introduced by the worst-case objective. We report several numerical experiments to illustrate convergence and risk-averse behavior.

Abstract: We give a fast algorithm for solving min-cost $k$-commodity flow. The basic idea is to construct an auxiliary linear program that has low rank and whose minimum value is at most $1/k$ times the minimum value of the original problem (thus, solving this auxiliary linear program will make at least $1/k$ fraction of progress in the original problem). Low-rank linear programs can be solved quickly using black-box techniques. Thus, our algorithm runs in time $\tilde{O}(\operatorname{poly}(k)(n^{2.5}+m\sqrt{n}))$ on a directed graph with $n$ vertices and $m$ edges. We do not rely on any fast matrix multiplication.

Abstract: We study many-to-one, two-sided stable matching problems in which preferences are complementary and firms and workers may rank the same allocation differently. Here a coalition is a group of workers that can be jointly matched with a firm. With complementary preferences, a stable matching need not exist. We show that a stable matching exists for every instance when two conditions hold. The first requires each firm to have an anchor worker who is included in every feasible coalition that can be matched with that firm. The second is Transitive Alignment, which means there must be an overall ranking across different coalitions that is consistent with the workers' preferences. We propose CDAR (Combinatorial Deferred Acceptance with Reproposals), a Deferred Acceptance-style algorithm that permits reproposals, and prove its finite-time convergence and its output of a stable matching by constructing an $N$-digit potential function. Moreover, we show that, under strict preferences, the output of CDAR is Pareto optimal among stable matchings. The proposed framework naturally captures applications such as vehicle-route assignment for traffic safety and the misaligned interests of labor and management in wage negotiation.

Abstract: The electric autonomous dial-a-ride problem (EADARP) extends the classical dial-a-ride problem by incorporating battery and charging constraints for electric vehicles. In practice, travel-time uncertainty can cause violations of time-window constraints. Large neighborhood search is effective for solving the EADARP, but its performance can depend on the choice of insertion operator during the repair phase. This paper investigates insertion-operator selection within a bilevel large neighborhood search framework for deterministic and chance-constrained variants of the EADARP. In the chance-constrained variant, arc travel times are modeled as independent normally distributed random variables, and upper time-window constraints are enforced probabilistically. We consider six selection methods, namely fixed greedy insertion, fixed regret-based insertion, random selection, a deterministic state-based rule, performance-adaptive ALNS selection, and LLM-based state-aware selection. Experimental results show comparable performance on smaller instances, while differences become more evident on larger and more constrained instances. There is no single strategy that performs best across all instances, and the relative performance of the LLM-based, rule-based, and ALNS strategies varies with the problem instance and experimental setting.

Abstract: Background: We address the problem of planning when the set of feasible states or actions changes over time. For example, in the problem of path planning among moving obstacles (sometimes known as SIPP), the feasibility of being at a particular location can change as the obstacles move. Or, the action of boarding a particular train is feasible only while it is stopped at the station. This dynamism means that the optimal plan and its duration can change depending on when execution begins. In practice, execution start time is often unknown until planning has completed or another agent gives the go-ahead. However, most prior planning work either ignores dynamism or assumes a known start time. This makes it straightforward to assess state and action feasibility but is impractical for some applications. Objectives: In this paper, we relax the assumption of a known start time. We define the setting of {\em any-start-time planning} and provide algorithms for it. Methods: We present a data structure called a compound arrival time function (cATF) that compactly encodes the optimal plan as a function of start time. We provide general-purpose planning algorithms, based on heuristic graph search, that assemble cATFs by propagating functions along edges instead of scalar costs. Results: We prove that the size of a cATF is at most linear in the problem size. An experimental evaluation of an implementation for the specific problem of SIPP shows that, on difficult problems, agents that rely on replanning often fail, while any-start-time algorithms using cATFs can quickly look up the optimal plan once the execution start time is known. Conclusions: By enabling efficient representations and reasoning for time-dependent plans, this work provides a foundation for planning in dynamic worlds.

Abstract: Time series forecasting (TSF) increasingly drives decisions in transportation, energy, finance, healthcare, and infrastructure, yet current evaluation remains overly narrow: standard benchmarks reward low held-out error, while robustness studies typically reduce failure to Gaussian noise, random masking, or bounded adversarial perturbations. This obscures the real failure modes of deployed forecasting systems. Input-side anomalies are not merely noisier inputs: they often reflect structured events that alter temporal dynamics, break cross-variable dependencies, induce regime shifts, or propagate from faulty sensors to downstream decisions. These semantic, causal, and system-level failures cannot be faithfully captured by i.i.d. perturbations alone. The rise of TSF foundation models makes this evaluation gap more urgent, as unauditable pretraining corpora make held-out generalization increasingly unreliable. We therefore advocate scenario-grounded stress testing. Each test instance should include historical inputs and future targets, together with a semantic scenario, an explicit failure operator, and a measurable difficulty level. This shift makes evaluation interpretable, attributable, and deployment-relevant and friendly, enabling the community to ask not only which model is accurate, but under what conditions it fails and why.

Abstract: We study the design of a token economy for highway lane allocation that aims to improve fairness without sacrificing traffic efficiency. Motivated by the San Mateo 101 Express Lanes Project, we consider a setting in which high-occupancy vehicles have unrestricted access to an express lane, while the remaining users can alternate between regular and express lanes by earning and spending nonmonetary tokens. We model the resulting interaction as a finite-population dynamic congestion game with heterogeneous time preferences and limited-information evolutionary policy revisions. Building on a mean-field approximation, we derive token prices that enforce the system-optimal lane split while inducing fairness over time through turn-taking. The scheme is evaluated in a microscopic traffic simulation with real-world demand data. The results show that the proposed prices yield nearly the same average travel time as a baseline scenario in which no lane is reserved as an express lane, while substantially reducing urgency-weighted perceived travel time. These findings highlight token economies as a promising alternative to monetary congestion pricing for fairer management of scarce road capacity.

Abstract: Cooperative perception, in which connected vehicles and roadside infrastructure share sensor information, is a candidate enabler of automated mobility, and benchmark accuracy is the evidence cited when roadside deployment is considered. This paper audits that evidence base across one simulated and two real-world vehicle-to-everything (V2X) benchmarks. In simulation, two widely studied robustness axes leave almost no recoverable headroom: an infrastructure-anchored pose correction returns about one accuracy point at every error level, and corrupting a partner costs 0.7 points. On real data, measurement choices govern the conclusion. An apparent seventeen-fold advantage of infrastructure in partner-poor frames falls below four-fold once the split is broadened, and an ad-hoc class definition measures a far smaller benefit than the official protocol reports. Cooperation is worth 7 to 15 accuracy points, yet 27% of frames on one split offer no partner and almost none do on another, so every regime-conditioned claim must name its split.

Abstract: We consider fair resource allocation in sequential decision-making environments modeled as major-minor weakly coupled Markov decision processes (M2WCMDP). In this framework, resource constraints couple the action spaces of a major sub-Markov decision process (sub-MDP) and a population of minor sub-MDPs that would otherwise operate independently. Instead of using the traditional utilitarian (total-sum) objective, we optimize a general class of monotone, concave, permutation-invariant, normalized fairness functions. With homogeneous minor sub-MDPs, we prove that the problem under symmetry reduces to optimizing the platform-plus-mean-participant utilitarian objective over the class of \textit{permutation-invariant} policies, which allows us to exploit efficient algorithms that optimize the utilitarian-based objective to solve this fairness-aware problem. For more general settings, we introduce a count-proportion-based deep reinforcement learning approach with a priority-based sampler that generates feasible count actions. The generality of our framework means that the proposed algorithms and theoretical guarantees transfer to any domain with a symmetric M2WCMDP structure. We consider two applications: the machine replacement problem and the joint control of pricing and taxi relocation problem on a New York City-calibrated dataset. We validate our theoretical findings with comprehensive experiments, confirming the effectiveness of our proposed method in achieving strong fairness-aware performance while remaining scalable.

Abstract: The reliable prediction of passenger train delays is a critical component of railway management. While contemporary research frequently attempts to maximize absolute accuracy by deploying opaque deep learning architectures, the underlying data mechanics driving longitudinal predictive decay remain underexplored. Consequently, this study provides an explainable temporal robustness analysis of network-wide railway delay prediction. Focusing on the Dutch railway network, this research utilizes interpretable tree-based ensembles to integrate granular topological, environmental, and operational features. The overarching finding establishes that while feature-rich tree-based models improve simultaneous (within-month) prediction, predictive performance systematically degrades when evaluated across non-simultaneous (future) months. Furthermore, multi-horizon SHAP and dispersion analyses explicitly link this degradation to environmental feature volatility and instability within the statistical target definition. Ultimately, this thesis demonstrates that richer feature sets alone are insufficient to resolve long-term forecasting constraints, underscoring the necessity to transition toward dynamic, season-aware architectures anchored by absolute operational boundaries.

Abstract: Near-term quantum optimizers accommodate roughly a hundred binary variables, requiring large Quadratic Unconstrained Binary Optimization problems to be decomposed into hardware-sized subproblems while other variables remain fixed. Variables are typically selected by ranking the objective changes from individual flips. We show that this rule is uninformative once the incumbent is optimal under single-variable flips: every score represents a cost, while remaining improvements depend on overlooked pairwise interactions. A second-order expansion instead yields a prize-collecting densest-subgraph selection problem, solvable greedily in time linear in the number of variables, and two solver-free bounds bracketing the improvement achievable within a selected subset. On transportation networks from Chicago and Philadelphia, our rule with 16-variable subproblems outperforms random selection with 64, demonstrating that quadrupling device capacity cannot compensate for weaker selection. Replacing geometric adjacency with road-network connectivity widens the margin by a factor of 1.6-1.9. With the selection trace fixed, varying the fraction of subproblems solved on a 120-qubit device from zero to one leaves the final objective unchanged to six significant figures. At tested hardware-accessible sizes, gains therefore arise from selection rather than the backend. Hardware feasibility is limited by coupling terms: 120-variable problems fail to compile with 7,260 terms but succeed with 5,118. Compilation scales almost quadratically with term count and dominates execution cost, reaching 1,752 seconds versus 469 seconds of quantum processing.

Abstract: AI agents built on a few shared models increasingly act for many people. A shared forecast about others can align their choices and change how scarce capacity is allocated. We tested this feedback in a two-road congestion game. Adding one sentence warning that others might follow a routing tip made populations of 50 GPT agents crowd one road while avoiding the nearly empty alternative. Average travel time rose from 64 to 95 min, although any crowded-road agent could have saved 69 min by switching alone. The warning discouraged the very move it predicted. The pattern persisted for 100 rounds. Two other model families shifted the same way without locking onto one road. Twelve all-human groups (240 participants) stayed near balance under numerical reports or the tip and warning. In 24 mixed groups with a further 240 participants, imbalance grew with the share of agents in the registered analysis, while people increasingly took the road the agents avoided. Collective costs stayed below the allagent reference, but with 15 agents and 5 humans, agent seats averaged 80 min, compared with 44 min for human seats. Shared forecasts can thus sustain collective inefficiency among similar agents. A better group average can also hide an unequal burden. Evaluations of AI agents that share resources should test populations, treat messages as interventions and report who bears the costs.

Abstract: As electric vehicle (EV) adoption increases, ensuring efficient and well-distributed charging infrastructure has become a critical challenge. While many EV charging station location problem (CSLP) studies focus on minimizing costs or travel distance, it is crucial to consider the surrounding geospatial characteristics of existing stations that influence operational performance. This study proposes a geospatial artificial intelligence (GeoAI)-based framework that integrates high-dimensional EV-related geospatial data, including EV usage, land-use, population, and traffic attributes. We incorporate a variational autoencoder (VAE) and a graph convolutional network (GCN) into the model to capture similarities among existing charging stations, and to identify suitable locations for future stations. The VAE compresses high-dimensional EV input data into a low-dimensional latent space, and the GCN uses this latent representation to predict locations suitable for charging stations. Using real-world data from Bryan-College Station, Texas, US, the proposed model outperforms state-of-the-art baselines, achieving an F1-score of 0.87 in distinguishing existing station locations from non-station locations. The model also identifies 27 additional candidate locations that show geospatial characteristics similar to those of existing stations, based on a similarity score. We further evaluate two policy implementation scenarios, maximizing geospatial similarity and minimizing total travel distance, each yielding different outcomes aligned with distinct strategic objectives. The findings highlight the importance of incorporating spatial context into CSLP and provide valuable insights for future EV infrastructure planning, promoting both efficiency and accessibility in the rapidly growing electric mobility sector.

Abstract: In this paper, the parameterized complexity of the multiplicative $α$-spanner problem with independent weights and lengths on undirected graphs is considered for the first time. All prior FPT results (except one on DAGs) assume basic instances (i.e., with unit weights and lengths) and are parameterized in the stretch factor $α$ and the (in practice typically non-constant) number of removed edges. We show that several parameterizations do not allow FPT algorithms. However, our exclusion approach generalizes an existing algorithm for basic instances to arbitrary weights and lengths. It is parameterized by the total removed weight and a new tightness parameter. The latter is more precise than $α$ and allows us to also improve the best known result for basic instances. Our second algorithm, called inclusion approach, uses the natural parameterization in the spanner's total weight. We prove that this sole parameter leaves a W[2]-hard problem, but also show FPT algorithms exist when augmented with secondary parameters.

Abstract: Customers often specify acceptable time intervals for receiving a service. When service on a date entails a fixed activation cost, overlapping intervals allow joint service and cost sharing. Customers may nevertheless conceal flexibility by reporting a smaller interval, affecting both operating cost and its allocation. We ask whether an operator can select a core allocation at every reported profile without making concealment profitable. We establish sharp population boundaries for preventing such coalitional reductions. When intervals may be narrowed from either end, a core-selecting rule preventing such reductions exists if and only if there are at most three customers. With four or more customers, impossibility holds even under Pareto contraction-proofness, which excludes deviations making every contracting customer weakly better off and at least one strictly better off. The impossibility persists when each contracting customer conceals only an arbitrarily small fraction of her feasible interval. The boundaries change when either the earliest or latest acceptable date of every customer is verifiable. With common verified dates, equal sharing is core-selecting and prevents such reductions for any population size. When verified dates may differ, the boundary rises to five: such a rule exists for up to five customers, whereas with six or more no core-selecting rule prevents the contracting customers from reducing their combined payment. Under Pareto contraction-proofness, however, core selection is possible for every population size on either one-sided domain. Finally, the relaxations needed for approximate core selection and coalitional contraction-proofness must grow with population size.

Abstract: For an odd prime $p$, let $Γ(R)$ denote the zero-divisor graph associated with the finite local ring $R= \mathbb{F}_p[x]/\langle x^4 \rangle$, having $p^3 - 1$ vertices and size $|E(Γ(R))| = \frac{1}{2}(3p^4 - 4p^3 - p^2 + 2)$. Using an equitable 4-cell partition induced by the ideal filtration $\langle u^3 \rangle \subset \langle u^2 \rangle \subset \langle u \rangle$, we prove that $\operatorname{Spec}_A(Γ(R))$ decomposes into discrete levels $λ\in \{0, -1\}$ with multiplicities $p^3 - p^2 - 1$ and $p^2 - 3$, respectively, alongside three irrational roots of an irreducible cubic polynomial $P_3(λ) = 0$, yielding adjacency energy $ε(Γ(R)) = 4p^2 + \mathcal{O}(p)$. In contrast, the Laplacian spectrum is entirely integral: $\operatorname{Spec}_L(Γ(R)) = \{0^1, (p - 1)^{p^3 - p^2}, (p^2 - 1)^{p^2 - p - 1}, (p^3 - 1)^{p - 1}\}$. Consequently, the tree entropy satisfies $z(Γ(R)) = \ln p - \frac{1}{p} + \frac{\ln p}{p} + \mathcal{O}(\frac{\ln p}{p^2})$, with small-failure unreliability bounded by $p^2(p - 1)(1 - q)^{p-1}$. In linear consensus $\dot{x} = -Lx$, error trajectories decouple into three modal timescales $\{ (p^3 - 1)^{-1}, (p^2 - 1)^{-1}, (p - 1)^{-1} \}$ with algebraic connectivity $α(Γ(R)) = p - 1$ and steady-state $H_2$ error variance $H_2^2 = \frac{Kf(Γ(R))}{2n^2} = \frac{1}{2p} + \mathcal{O}(p^{-3})$. Furthermore, the Kirchhoff index yields a vanishing average resistance distance $\overline{r}(Γ(R)) = \frac{2}{p} + \mathcal{O}(p^{-3}) \to 0$, while unbiased Markovian random walks induce an asymptotic traffic concentration vector $Π= (\frac{1}{3}, 0, \frac{1}{3}, \frac{1}{3})$ with quadratic per-node core routing stress $π_{\mathrm{core}}/π_{\mathrm{periph}} \sim p^2 + p + 1$.

Abstract: Covariate-rich time-series forecasting requires deciding how external variables enter the target forecasting path. Existing Transformer-based forecasters usually build a covariate representation and pass it to the encoder without an explicit admission stage. This paper studies pre-encoder covariate admission as an input-side interface that regulates that representation immediately before encoder processing. We implement the interface with a lightweight representation-level pre-encoder gate that assigns sigmoid scores to representation units, and we also study a usage-regularized variant that penalizes average admission. The interface is evaluated as a plug-in module for TimeXer, Inverted Transformer (iTransformer), and Patch Time Series Transformer (PatchTST) under a zero-extra-tuning protocol, where each gated model inherits the corresponding baseline configuration. Experiments on the Electricity Transformer Temperature minute-level (ETTm1 and ETTm2) datasets, Traffic, Energy, and influenza-like illness (ILI) include paired forecasting comparisons, gate-placement ablation, initialization ablation, controlled covariate-admission analysis, and a variance inflation factor (VIF)-informed permutation feature importance (PFI) diagnostic case study. In the tested settings, the gate is competitive with the corresponding baselines, and the usage penalty reduces average admission scores while keeping forecasting errors close to the unpenalized TimeXer setting.

Abstract: Travel demand forecasting is essential for evaluating large-scale infrastructure projects, yet the traditional sequential four-step process can produce inconsistencies across trip distribution, mode choice, and traffic assignment. Although combined models address these inconsistencies, their practical use has been limited by simplified behavioral assumptions, computational burden, and the lack of a unified parameter-estimation framework. We propose a convex programming approach that integrates destination, mode, and route choices within a hierarchical extended logit model. The optimal primal solution characterizes the joint travel-demand equilibrium, while the optimal dual variables recover taste coefficients, alternative-specific constants, and destination- and mode-level scale parameters. The model captures mode correlations through nested logit and route overlap through path-size logit. Its convex structure provides global optimality guarantees and enables efficient solution using off-the-shelf conic solvers. Observed travel patterns are incorporated through moment and conditional-entropy constraints, while the route-level dispersion parameter is calibrated separately using partial link counts. Numerical experiments on eight benchmark networks demonstrate the scalability and computational efficiency of the formulation.

Abstract: Localized roadway incidents can produce congestion well beyond their point of origin, but evaluating these effects with microscopic simulation requires a separate run for each scenario. This paper presents a Spatio-Temporal Graph Convolutional Network (STGCN) for forecasting route-level travel times on a simulated Nashville, Tennessee road network with 1,037 junctions and 1,601 road segments. The model uses directional traffic counts from only 129 signalized intersections, reflecting data commonly available to transportation agencies. By representing these intersections as a graph, the STGCN jointly captures spatial dependence and temporal traffic evolution to learn how localized disruptions propagate through the network. We compare a baseline trained on 80 incident-free simulations with an incident-inclusive model trained with an additional 360 lane-blockage scenarios across 12 locations and three durations. The baseline achieved a relative mean absolute error (MAE) of 9.94%. The incident-inclusive model achieved 9.67% overall, 6.45% during active incidents, and 13.62% at 30 incident locations withheld entirely from training. On disrupted routes, its predictions were within 2.0 minutes of observed travel time on average. For comparison, simulated travel times vary by 7.4%, or 1.3 minutes, across random seeds under identical conditions. Inference requires approximately 53 ms on a single CPU core, demonstrating the potential of the model as an efficient surrogate for transportation resilience screening, incident management, and proactive rerouting.

Abstract: Strong Connectivity Augmentation (SCA) asks whether a directed acyclic graph can be made strongly connected by adding at most $k$ prescribed links whose total weight is within a given budget. Klinkby, Misra, and Saurabh (SODA 2021) gave an $O^*(2^{O(k\log k)})$-time algorithm and asked whether the problem admits a single-exponential parameterized algorithm and a polynomial kernel. We answer both questions affirmatively: SCA can be solved in $O^*(9^k)$ time and admits a polynomial kernel with $O(k^4)$ vertices and $O(k^{16})$ bits. For unweighted SCA, we obtain $O^*(4^k)$ time and a kernel with $O(k^3)$ vertices. Our algorithms are based on a particularly simple reduction to Strongly Connected Spanning Subgraph with two edge costs.

Abstract: We introduce cooperative integer programming games (CIPGs), in which agents pool budget constraints to accomplish indivisible tasks jointly and the characteristic function maps every coalition to the optimal value of a pooled integer program. Our goal is to identify an optimal coalition structure (OCS) and a stable one (OSCS). We derive a stability inequality that keeps each formed coalition in the Core with respect to itself, and present two mixed-integer OCS formulations, aggregated and disaggregated, proving that the disaggregated formulation is integer-equivalent yet yields a tighter LP relaxation. Building on the stability inequality we develop lifted stability cuts, several separation strategies inside a cutting-plane algorithm, an SCS-feasible primal heuristic that constructs warm starts with guaranteed stability, and a payoff-refinement step computing the Shapley value and the nucleolus of every formed coalition. On benchmark cooperative knapsack games, the method certifies optimality with up to 16 players and reaches MIP gaps below 1% at 30 players while evaluating 766 of the roughly $10^9$ coalition values.

Abstract: Travel survey data are essential for transportation planning and travel behavior analysis, yet collecting large-scale representative samples is costly and time-consuming. A practical alternative is to generate synthetic survey records from a few-shot sample. However, such samples provide incomplete coverage of heterogeneous traveler groups and insufficient evidence for recovering the complex dependencies between demographic characteristics and travel behavior. Existing approaches have complementary limitations. Probabilistic generative models such as Bayesian networks (BNs) offer explicit distributional control, but structures learned from few-shot samples may omit meaningful dependencies or retain spurious ones. Large language models (LLMs) can help address these difficulties in BN structure learning by providing behavioral knowledge that complements the limited statistical evidence. We therefore propose LEBGen, an LLM-enhanced BN framework that uses this knowledge to refine network structure for few-shot travel survey data generation. Specifically, the LLM first identifies traveler personas from demographic attribute and travel behavior statistics, then recovers dependencies missed by the persona-augmented BN structure and prune spurious ones. The refined BN is parameterized exclusively from the observed data to generate synthetic records. Under a 2% few-shot setting on the 2022 Hong Kong Travel Characteristics Survey, LEBGen reduces the mean marginal Jensen-Shannon divergence from 0.0671 to 0.0091 and the mean absolute Cramer's V error by 14.3% over the best-performing baseline, substantially improving both distributional and dependency fidelity.