Related papers: Worst-Case to Expander-Case Reductions
The notion of augmenting graphs generalizes Berge's idea of augmenting chains, which was used by Edmonds in his celebrated solution of the maximum matching problem. This problem is a special case of the more general maximum independent set…
We design improved approximation algorithms for NP-hard graph problems by incorporating predictions (e.g., learned from past data). Our prediction model builds upon and extends the $\varepsilon$-prediction framework by Cohen-Addad, d'Orsi,…
The minimum $s$-$t$ cut problem in graphs is one of the most fundamental problems in combinatorial optimization, and graph cuts underlie algorithms throughout discrete mathematics, theoretical computer science, operations research, and data…
The graph is one of the most widely used mathematical structures in engineering and science because of its representational power and inherent ability to demonstrate the relationship between objects. The objective of this work is to…
We study a large family of graph covering problems, whose definitions rely on distances, for graphs of bounded cyclomatic number (that is, the minimum number of edges that need to be removed from the graph to destroy all cycles). These…
We introduce the balanced crown decomposition that captures the structure imposed on graphs by their connected induced subgraphs of a given size. Such subgraphs are a popular modeling tool in various application areas, where the non-local…
Dense subgraph extraction is a fundamental problem in graph analysis and data mining, aimed at identifying cohesive and densely connected substructures within a given graph. It plays a crucial role in various domains, including social…
A natural way of increasing our understanding of NP-complete graph problems is to restrict the input to a special graph class. Classes of $H$-free graphs, that is, graphs that do not contain some graph $H$ as an induced subgraph, have…
The Small-Set Expansion Hypothesis (Raghavendra, Steurer, STOC 2010) is a natural hardness assumption concerning the problem of approximating the edge expansion of small sets in graphs. This hardness assumption is closely connected to the…
The \emph{Dominating $H$-Pattern} problem generalizes the classical $k$-Dominating Set problem: for a fixed \emph{pattern} $H$ and a given graph $G$, the goal is to find an induced subgraph $S$ of $G$ such that (1) $S$ is isomorphic to $H$,…
There has been significant recent progress on algorithms for approximating graph spanners, i.e., algorithms which approximate the best spanner for a given input graph. Essentially all of these algorithms use the same basic LP relaxation, so…
We present a prototype of a software tool for exploration of multiple combinatorial optimisation problems in large real-world and synthetic complex networks. Our tool, called GraphCombEx (an acronym of Graph Combinatorial Explorer),…
Graph partitioning is a fundamental combinatorial optimization problem that attracts a lot of attention from theoreticians and practitioners due to its broad applications. From multilevel graph partitioning to more general-purpose…
We introduce a graph decomposition which exists for all simple, connected graphs $G=(V,E)$. The decomposition $V = A \cup B \cup C$ is such that each vertex in $A$ has more neighbors in $B$ than in $A$ and vice versa. $C$ is `balanced':…
Given a graph $G$, the maximal induced subgraphs problem asks to enumerate all maximal induced subgraphs of $G$ that belong to a certain hereditary graph class. While its optimization version, known as the minimum vertex deletion problem in…
Which transformer scaling regimes are able to perfectly solve different classes of algorithmic problems? While tremendous empirical advances have been attained by transformer-based neural networks, a theoretical understanding of their…
This paper proposes a new general technique for maximal subgraph enumeration which we call proximity search, whose aim is to design efficient enumeration algorithms for problems that could not be solved by existing frameworks. To support…
Decomposing hypergraphs is a key task in hypergraph analysis with broad applications in community detection, pattern discovery, and task scheduling. Existing approaches such as $k$-core and neighbor-$k$-core rely on vertex degree…
How to obtain a graph from data samples is an important problem in graph signal processing. One way to formulate this graph learning problem is based on Gaussian maximum likelihood estimation, possibly under particular topology constraints.…
We are interested in multilayer graph clustering, which aims at dividing the graph nodes into categories or communities. To do so, we propose to learn a clustering-friendly embedding of the graph nodes by solving an optimization problem…