Related papers: Efficient Enumerations for Minimal Multicuts and M…
Node classifiers are required to comprehensively reduce prediction errors, training resources, and inference latency in the industry. However, most graph neural networks (GNN) concentrate only on one or two of them. The compromised aspects…
Normalized-cut graph partitioning aims to divide the set of nodes in a graph into $k$ disjoint clusters to minimize the fraction of the total edges between any cluster and all other clusters. In this paper, we consider a fair variant of the…
In Directed Multiway Cut(Dir-MC) the input is an edge-weighted directed graph $G=(V,E)$ and a set of $k$ terminal nodes $\{s_1,s_2,\ldots,s_k\} \subseteq V$; the goal is to find a min-weight subset of edges whose removal ensures that there…
MaxCut is a classical NP-complete problem and a crucial building block in many combinatorial algorithms. The famous Edwards-Erd\H{o}s bound states that any connected graph on n vertices with m edges contains a cut of size at least $m/2 +…
We consider the \textsc{Edge Multiway Cut} problem on planar graphs. It is known that this can be solved in $n^{O(\sqrt{t})}$ time [Klein, Marx, ICALP 2012] and not in $n^{o(\sqrt{t})}$ time under the Exponential Time Hypothesis [Marx,…
Motivated by hypergraph decomposition algorithms, we introduce the notion of edge-induced vertex-cuts and compare it with the well-known notions of edge-cuts and vertex-cuts. We investigate the complexity of computing minimum edge-induced…
We consider the problem of finding edge-disjoint paths between given pairs of vertices in a sufficiently strong $d$-regular expander graph $G$ with $n$ vertices. In particular, we describe a deterministic, polynomial time algorithm which…
Finding an optimal subset of nodes or links to disintegrate harmful networks is a fundamental problem in network science, with potential applications to anti-terrorism, epidemic control, and many other fields of study. The challenge of the…
We investigate the single source shortest distance (SSSD) and all pairs shortest distance (APSD) problems as enumeration problems (on unweighted and integer weighted graphs), meaning that the elements $(u, v, d(u, v))$ -- where $u$ and $v$…
We study algorithmic and structural aspects of connectivity in hypergraphs. Given a hypergraph $H=(V,E)$ with $n = |V|$, $m = |E|$ and $p = \sum_{e \in E} |e|$ the best known algorithm to compute a global minimum cut in $H$ runs in time…
Given an edge-weighted graph, how many minimum $k$-cuts can it have? This is a fundamental question in the intersection of algorithms, extremal combinatorics, and graph theory. It is particularly interesting in that the best known bounds…
We present near-optimal algorithms for detecting small vertex cuts in the CONGEST model of distributed computing. Despite extensive research in this area, our understanding of the vertex connectivity of a graph is still incomplete,…
The shortest path problem in graphs is a cornerstone of AI theory and applications. Existing algorithms generally ignore edge weight computation time. We present a generalized framework for weighted directed graphs, where edge weight can be…
It is a long-standing open problem whether the minimal dominating sets of a graph can be enumerated in output-polynomial time. In this paper we investigate this problem in graph classes defined by forbidding an induced subgraph. In…
The distinguishing result of this paper is a $\mathbf{P}$-time enumerable partition of all the potential perfect matchings in a bipartite graph. This partition is a set of equivalence classes induced by the missing edges in the potential…
We consider the (exact, minimum) $k$-cut problem: given a graph and an integer $k$, delete a minimum-weight set of edges so that the remaining graph has at least $k$ connected components. This problem is a natural generalization of the…
Despite the success of graph neural network models in node classification, edge prediction (the task of predicting missing or potential links between nodes in a graph) remains a challenging problem for these models. A common approach for…
Hyperbolicity is a graph parameter which indicates how much the shortest-path distance metric of a graph deviates from a tree metric. It is used in various fields such as networking, security, and bioinformatics for the classification of…
The All-Pairs Min-Cut problem (aka All-Pairs Max-Flow) asks to compute a minimum $s$-$t$ cut (or just its value) for all pairs of vertices $s,t$. We study this problem in directed graphs with unit edge/vertex capacities (corresponding to…
There has recently been much progress on exact algorithms for the (un)weighted graph (bi)partitioning problem using branch-and-bound and related methods. In this note we present and improve an easily computable, purely combinatorial lower…