May 2026· IEEE International Conference on Data Engineering· pp. 2545-2558· 0 citations· 73 references
Abstract
Cohesive subgraph mining is a fundamental task in graph data analytics. We re-visit the problem of listing all minimal $k$-cores, where a $k$-core is a subgraph in which every vertex has degree at least $k$, and minimality requires that no proper subset remains a $k$-core. Existing methods are computationally prohibitive due to explosive branching and costly branch state update, leading to the trivial worst-case bound $O^{*}\left(2^{n}\right)$ for the basic branch-and-bound baseline wh, where $O^{*}$ suppresses polynomial factors and $n$ is the number of vertices. In this paper, we present an improved method IMinC based on three key ideas: (i) a principled branching state with lineartime update; (ii) a pivot strategy that guides branching toward promising vertices; and (iii) a divide-and-conquer framework that initializes each subproblem to enable our pivot strategy throughout and reduce recursion depth. We further introduce three reduction rules that aggressively prune infeasible branches. Together, these components yield the worst-case time complexity of $O^{*}\left(\alpha_{\ell}^{n}\right)$, where $\alpha_{\ell}$ is a positive number strictly smaller than 2. We also extend IMinC to list minimal $k$-cores under a size bound, addressing practical needs such as size-bounded community search. Extensive experiments on 12 real-world graphs demonstrate that IMinC outperforms the baselines by up to 2 order of magnitude, delivering substantial gains in efficiency.
In the cut-query model, an algorithm is given access to a graph $G = (V, E)$ \emph{only} via cut queries. This model has seen significant attention in the undirected graph setting, with works establishing $O(n)$ cut query algorithms for computing the global minimum cut, $\widetilde{O}(n^{3/2})$ cut query algorithms for all pairs minimum cut, and many more. However, despite this vast array of progress in designing sub-quadratic query algorithms for computing properties of undirected graphs, there has been \emph{no} progress in designing such algorithms in directed graphs. Indeed, even for basic problems like whether a vertex $t$ is reachable from a vertex $s$, the cut query complexity is only known to be bounded in the interval $[\Omega(n), O(n^2 / \log n)]$. In this work, we begin a systematic study of these basic problems in directed \emph{acyclic} graphs (DAGs). In this setting, we show that reachability from a single vertex and even topological sorting are both computable in $O(n \log^3 n)$ many cut queries. As a consequence, we also obtain an algorithm which, for any \emph{arbitrary} directed graph $G$, uses only $O(n \log^3 n)$ cut queries and determines whether $G$ contains a cycle.
This paper provides the first truly linear-time approximation scheme for the Densest Subgraph Problem, and uses assignments arising from a flow-based formulation together with a structural carving lemma to progressively carve "sparse" parts of the graph while nearly preserving the densest subgraph.
The subgraph reconfiguration problem asks whether one subgraph can be transformed into another via a sequence of local changes while maintaining a specified graph property. In this work, we focus on the setting where the subgraph is specified by its set of edges. Our contributions in this paper are twofold. First, motivated by the contrast that path reconfiguration is $\textsf{NP}$-hard while tree reconfiguration is solvable in linear time, we prove two generalizations: (1) for any fixed $k$ at least one, reconfiguring connected graphs with pathwidth at most $k$ is $\textsf{NP}$-hard, and (2) for any fixed $k$ at least two, reconfiguring graphs with pathwidth at most $k$ is also $\textsf{NP}$-hard. En route to proving (2), we show a general hardness result that applies to a range of minor-closed graph classes, which we use to show planar graph reconfiguration is also $\textsf{NP}$-hard. Second, given our negative results, we extend the problem to a resource-focused setting, asking how much additional buffer space is needed to turn a non-reconfigurable instance into a reconfigurable one. We show that $\Omega(n)$ extra buffer space is needed for planar graphs and graphs with bounded pathwidth and treewidth, while $O(1)$ extra buffer space is sufficient for cactus graphs in a restricted setting.
It is proved that Minimal-to-Maximal Conversion Search is in fact not output-polynomial and the lower bound construction motivates a more detailed analysis of how certain heuristic choices in the algorithm design affect the running time.
We give a randomized data structure for undirected weighted graphs that are partially dynamic, i.e., that undergo either only edge insertions or only edge deletions. The data structure maintains $(1\pm\epsilon)$-approximations to the maxflow value and effective resistance between any queried pair of vertices, with total update time $\widetilde{O}_{\epsilon}(n^2)$ and worst-case query time $\widetilde{O}_{\epsilon}(1)$. Thus, for dense graphs where $m = \Omega(n^2)$, our guarantees are near-optimal. Our algorithms succeed with high probability against an adaptive adversary. Our result follows from a simple stability principle for partially dynamic graphs. We show how to partition an online sequence of $m$ updates into $\widetilde{O}(n/\epsilon)$ epochs such that every graph within an epoch is a $(1\pm O(\epsilon))$-spectral approximation of the graph at the beginning of the epoch. The epochs are determined by the cumulative leverage score of the updated edges: small leverage-score mass implies small spectral change, while the total leverage-score mass over a monotone update sequence is $\widetilde{O}(n)$. Consequently, a spectral sparsifier needs to be recomputed only once per epoch. Applying known static all-pairs maxflow and effective-resistance oracles to these sparsifiers then yields the result.
Gramoz Goranci, Rasmus Kyng, Maximilian Probst Gutenberg et al.· 0 citations
A representative possible world (RPW) is a deterministic graph derived from an uncertain graph $\mathcal{G}$ where a designated structural feature closely approximates its expected value in $\mathcal{G}$. Serving as a proxy for $\mathcal{G}$, the RPW allows conventional deterministic algorithms to be directly executed on it for mining tasks targeting this feature, thereby avoiding computationally expensive enumeration or sampling on $\mathcal{G}$. Existing studies on RPWs primarily focus on individual node features, e.g., degree or triangle degree. However, many mining tasks, such as link prediction, critically rely on the number of common neighbors between two nodes, which is a pairwise feature. To bridge this gap, we study the \underline{C}ommon-neighbor-count-based \underline{R}epresentative \underline{P}ossible \underline{W}orld (CRPW) problem, extending RPWs from preserving node-level statistics to preserving pairwise structural relationships. The problem seeks the possible world that best preserves the expected numbers of common neighbors between node pair, and we prove that is NP-hard. To address it, we develop a two-stage basic algorithm that quickly initializes a possible world and then refines it iteratively. We next accelerate the refinement by replacing its costly floating-point evaluation with an efficient integer counting strategy, as the refinement only requires determining whether a change is beneficial, rather than computing its exact magnitude. Moreover, we design a Beta-based adaptive termination method to automatically stop the refinement once the desired quality of the possible world is reached, preventing over- or under-execution. Extensive experiments on real-world uncertain graphs demonstrate the effectiveness of our algorithms on diverse mining tasks. Especially on common-neighbor-related tasks, we achieve the best performance among all compared methods.
Chengjie Gu, Xiaoliang Xu, Yuxiang Wang et al.· 0 citations