network engineers

Abstract: Federated learning over IEEE~802.11 shares the wireless channel among clients that send model updates. We use ns-3 to measure the frame-delivery ratio and saturation throughput for different client densities and offered loads. A separate FedAvg trainer uses the frame-delivery ratio as a first-order proxy for the update-admission probability and uses an equation to estimate communication time. The method does not simulate the delivery of a complete model update or measure end-to-end training time. Across 720 evaluated runs with two datasets, two data partitions, six client densities, six offered loads, and five seeds, all runs reached their predefined target accuracy within the round budget. Rounds-to-target changed little with offered load, while communication time-to-target increased by about two orders of magnitude across the client-density range. A Bianchi-anchored estimator produced a mean absolute percentage error from $2.3\%$ to $10.2\%$ on held-out configurations. This error is measured against communication time constructed from the same round-duration equation, not against independently measured completion time. We also compare uniform participation with persistent heterogeneous participation. The study does not detect a statistically distinguishable excluded-class accuracy gap over five seeds, but the confidence intervals are wide. The results apply only to the evaluated configurations and do not provide a general convergence or fairness guarantee.

Abstract: Finding large lattice subgraphs in sparse Erdős--Rényi random graphs is a classical problem at the interface of random graph theory and algorithms. General bounded-degree embedding and universality theorems give powerful results for broad graph families, but when specialized to square grids they operate at densities substantially larger than the grid-emergence scale. In this paper we exploit the specific geometry of the square grid. We introduce the Quarantined Local Search, a three-phase local algorithm that separates the construction of an initial boundary from the later corner-closure process and controls adaptive negative exposure through bounded pair-test histories. We prove that, for every fixed $δ\in (0,1)$, there exists $C_δ>0$ such that the algorithm embeds a $k\times k$ square grid with $k^2\le (1-δ)n$ in $G(n,p)$ with high probability whenever $p\ge C_δ\sqrt{\ln k/n}$. Thus, for $k^2=Θ(n)$, a density of order $\sqrt{\log n/n}$ is sufficient, a factor of order $\sqrt{\log n}$ above the corresponding $n^{-1/2}$ emergence scale.

Abstract: We determine a sharp threshold for the adaptable 2-colorability of a random graph equipped with a uniformly random, not necessarily proper, red/blue coloring of the edges. To accomplish this, we characterize a family of subgraphs along with edge colorings whose inclusion or exclusion determines adaptable $2$-colorability. We further show that above the threshold, a long path with alternating edge colors is formed. We use this path to prove the existence of such a subgraph in the supercritical regime. We then provide and prove symmetric bounds on the critical window for $2$-adaptable colorability. Particularly, we prove bounds matching that of the critical windows for the giant component in the Erd$ő$s-R$é$nyi random graph model as well as the satisfiability of a random $2$-SAT instance. Finally, we show that below the critical window, the solution space of adaptable $2$-colorings remains connected, that is one can travel from one adaptable $2$-coloring to another by a sequence of $2$-colorings which differ on $O(\log{n})$ many vertices.

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: This paper investigates the performance of high-altitude platform station (HAPS)-assisted communication systems employing either reconfigurable intelligent surfaces (RIS) or relay stations (RS) under non-orthogonal multiple access (NOMA) scheme. Practical system impairments, including hardware impairments (HWI) and imperfect channel state information (CSI), are explicitly considered. The results show that HAPS-RIS outperforms HAPS-RS in terms of both sum-rate and energy efficiency under non-ideal conditions due to its passive nature, which avoids noise amplification. Furthermore, it is demonstrated that RIS element allocation and user spatial distribution significantly impact NOMA performance, where increased user separation and proper allocation enhance channel disparity and improve system efficiency. Despite its higher sensitivity to imperfect CSI, HAPS-RIS can effectively compensate for performance degradation through large-scale RIS element deployment, maintaining a performance advantage over half-duplex RS-based systems. These insights provide useful design guidelines for impairment-aware HAPS-assisted 6G communication systems.

Abstract: We study the \emph{vantage point selection} problem, introduced by Ashvinkumar, Chowdhury, Gao, Goswami, Mitchell, and Polishchuk [WADS'25] to model the problem of estimating bottleneck capacities on the Internet. The input is a weighted undirected graph with unique shortest paths where every edge has a distinct unknown \emph{capacity}. When the algorithm \emph{queries} a vertex $v$, it reveals the minimum-capacity edge on the shortest path from $v$ to every other vertex reachable from $v$. The goal is to maximize the total number of revealed edges. The quality of an algorithm is measured by its competitive ratio against an optimal algorithm that knows all edge capacities a priori. We first consider the foundational single-query setting, where both the algorithm and the optimal algorithm are restricted to a single query. There is a trivial upper bound of $O(n)$ on the competitive ratio and the best known lower bound was $\tildeΩ(\sqrt{n})$. We provide an algorithm and matching lower bound (up to polylogarithmic factors) showing that the best possible competitive ratio is $\tildeΘ(n^{2/3})$. Furthermore, we extend our results to the general setting where the optimal algorithm is allowed $k$ queries and our algorithm is allowed $αk$ queries for $α\geq 1$. We present a randomized non-adaptive algorithm and matching lower bound (up to polylogarithmic factors) showing that the best possible expected competitive ratio for non-adaptive algorithms is the following surprisingly complex bound: $$ \tildeΘ\left( \min\left\{ \frac{n}{αk}, \max\left( \sqrt{\frac{n}α}, \frac{n^{2/3}}{αk^{1/3}} \right) \right\} \right). $$

Abstract: Let $λ$ be the minimum cut value of an $n$-vertex undirected multigraph. For every fixed $α>1$, we prove that there are $O(n^{\lceil2α\rceil-1})$ cuts of size strictly below $αλ$. The exponent is sharp. The proof combines splitting off and sampling with a bound on the size of nested families of vertex sets.

Abstract: Existing knowledge-base-assisted semantic communication schemes commonly adopt either single knowledge-base quantization (SKBQ) or multi-knowledge-base residual quantization (MKBQ). SKBQ incurs limited storage overhead but has restricted quantization capacity, whereas MKBQ supports progressive refinement by assigning an independent knowledge base (KB) to each stage, causing the KB storage to grow linearly with the transmission depth. To address this problem, we propose storage-scalable knowledge-base reuse quantization (SSKBQ), which reuses a compact set of KBs across multiple residual refinement stages and thereby decouples the number of transmission stages from the number of maintained KBs. A stage-aware residual supervision mechanism is further introduced to regularize intermediate quantized representations and encourage progressive refinement. Experimental results demonstrate that KB reuse provides an effective solution to the storage scalability problem while maintaining competitive progressive reconstruction performance.

Abstract: For a graph $H$, the $H$-freeness edge-deletion problem is the algorithmic problem of finding, for an input graph $G$, the minimum number of edges of $G$ whose deletion turns $G$ into an $H$-free graph. We show that for every graph $H$ containing a cycle, this problem is NP-hard. This proves a conjecture of Gishboliner, Levanzov and Shapira, and completes the characterization of the complexity of the $H$-freeness edge-deletion problem, answering a question of Alon, Shapira and Sudakov.

Abstract: Local similarity indices are widely used in link prediction on complex networks owing to their low computational cost; however, in sparse networks they assign a zero score to every node pair lacking common neighbors, which severely limits their predictive power. A natural remedy is to fuse node centrality indices with local similarity indices: the former provide global importance for the node pair, while the latter capture fine-grained local topology, and the two can be combined into complementary scores within a unified framework. This paper uses PageRank and DomiRank as two representative centrality measures and constructs a centrality--local-similarity fusion framework. The PageRank-based fusion proposed by Charikhi is first generalized to seven classical local similarity indices, and the universality of its improvement is systematically verified on nine real-world network datasets. Furthermore, the DomiRank centrality is introduced to build the DR-MD series of fused indices under a unified weighting coefficient, which overcomes the drawback that the PageRank-based fusion requires index-by-index weight tuning. Results of five-fold cross-validation together with Wilcoxon signed-rank tests show that, under the unified experimental protocol, all DR-MD indices consistently outperform the corresponding local baselines and their PR-MD counterparts on all nine datasets ($p=0.002$), and that the improvements remain robust against perturbations of $σ$ and the weighting coefficients within the near-critical parameter plateau; in particular, DR-RA achieves an average AUC of 0.7084, surpassing global methods such as Katz and RWR as well as several advanced similarity indices. The framework is inherently extensible, and its fusion paradigm can be straightforwardly generalized to couple other node centrality indices with local similarity indices.

Abstract: Let $X$ be a finite set with $|X|=n$ and let $\mathrm{Jac}(a,b)=|a\,\triangle\, b|/|a\cup b|$ be the Jaccard distance on the power set $2^X$. Lladser and Paradise recently proved that the metric dimension of $(2^X,\mathrm{Jac})$ is $Θ(n/\ln n)$, with the constant left open; their bounds are $(\ln 2)\,n/\ln n\lesssim β(2^X,\mathrm{Jac})\lesssim 2\ln(2e)\,n/\ln n$. We determine the constant: \[ β(2^X,\mathrm{Jac})=\frac{2n}{\log_2 n}\,(1+o(1))=(2\ln 2)\,\frac{n}{\ln n}\,(1+o(1)). \] The proof identifies the problem, on each ``slice'' of subsets of fixed cardinality, with the Erdős--Rényi coin-weighing problem for a spring scale (the problem of \emph{detecting matrices}). The lower bound is the Erdős--Rényi entropy argument applied to the middle slice; the upper bound follows from the explicit detecting families of Lindström and of Cantor and Mills, augmented by a single extra landmark that reveals cardinality.

Abstract: For an undirected graph $G = (V,E)$ and a fault bound $f$, an edge-fault-tolerant connectivity labeling scheme assigns short labels to vertices and edges, so that for any vertex pair $(s,t)$ and failed edge set $F\subseteq E$ with $|F|\leq f$, the connectivity between $s$ and $t$ in $G-F$ can be answered by inspecting only the labels of $s$, $t$ and edges in $F$. In this paper, we present a labeling scheme that uses $O(\log^{2}n)$-bit labels that can be computed in deterministic polynomial time. This improves upon the previous $\tilde{O}(\sqrt{f})$ deterministic bound of [Long, Pettie, Saranurak'25], and even slightly improves the $O(\min\{f+\log n,\log^{2}n\log f\})$ randomized bound of [Dory, Parter'21] and [Long, Pettie, Saranurak'25] when $f = Ω(\log^{2}n)$. Moreover, for a general $f$, this is the first labeling scheme that produces an $\tilde{O}(1)$-size labeling which is simultaneously correct across all queries. Our approach combines the cycle-space-based labeling scheme from Dory and Parter with a recent result by [Knauer'26] on sparse cycle bases.

Abstract: Higher-order structures offer a natural representation of complex systems that involve interactions between groups of different sizes. A widespread feature of their higher-order structure is nestedness, whereby interactions involving smaller groups are contained within larger ones. Yet, why interactions of different orders organise into nested structures remains largely unexplained. Here, we introduce an analytically tractable geometric model of higher-order networks in which a single latent geometric space couples interactions across orders, leading to the spontaneous emergence of nestedness. We show analytically and numerically that nestedness undergoes a transition between a nested geometric regime, where it remains finite in the thermodynamic limit, and a regime where it vanishes with system size. In this regime, we uncover a weakly geometric range characterized by an anomalously slow finite-size decay, allowing substantial nestedness to persist in finite systems even when its asymptotic value vanishes. Finally, with a single geometric coupling parameter, the model reproduces the nestedness profiles observed in real-world hypergraphs across different domains. Our results reveal latent geometry as a simple organising principle underlying the nested organisation of higher-order interactions.

Abstract: Given a graph $G=(V,E)$, let $S$ ($\subseteq V$) be a set of vertices. Two vertices are \emph{mutually visible} if there exists a shortest path in $G$ between them that does not contain any other vertex of $S$. A set $S$ is a \emph{Mutual Visibility Set} (\MVS) if every pair of vertices in $S$ is mutually visible. The concept of \MVS s in graphs has attracted significant attention since its introduction, as it provides an important structural property of graphs. However, determining a maximum \MVS\ in general graphs is computationally intractable; the decision problem of whether a graph admits an \MVS\ of size at least $k$ has been shown to be \emph{NP-complete}. Thus, prior work has focused on finding maximal \MVS s or restricting attention to specific graph classes. Cactus graphs form a fundamental low-treewidth class, yet the maximum \MVS\ problem for this class remains open. In this paper, we first determine the size of maximum \MVS~in cactus graphs, and introduce two self-stabilizing algorithms that construct such sets. The first algorithm uses a single BFS tree and stabilizes in $O(D)$ rounds with $O(\log n)$ bits per process on average; the second one uses parallel BFS trees and stabilizes in $O(|C_{\max}|+|T_{\max}|)$ rounds, which we show to be asymptotically tight as a function of these two parameters, even on graphs where $|C_{\max}|+|T_{\max}| = o(D)$.