Related papers: Fast Factorization of Cartesian products of Hyperg…
This paper is concerned with the recognition of approximate graph products with respect to the Cartesian product. Most graphs are prime, although they can have a rich product-like structure. The proposed algorithms are based on a local…
Cut and spectral sparsification of graphs have numerous applications, including e.g. speeding up algorithms for cuts and Laplacian solvers. These powerful notions have recently been extended to hypergraphs, which are much richer and may…
In graph theory, the longest path problem is the problem of finding a simple path of maximum length in a given graph. For some small classes of graphs, the problem can be solved in polynomial time [2, 4], but it remains NP-hard on general…
A \emph{disk graph} is the intersection graph of (closed) disks in the plane. We consider the classic problem of finding a maximum clique in a disk graph. For general disk graphs, the complexity of this problem is still open, but for unit…
In an $r$-uniform hypergraph on $n$ vertices a tight Hamilton cycle consists of $n$ edges such that there exists a cyclic ordering of the vertices where the edges correspond to consecutive segments of $r$ vertices. We provide a first…
In the classic Maximum Weight Independent Set problem we are given a graph $G$ with a nonnegative weight function on vertices, and the goal is to find an independent set in $G$ of maximum possible weight. While the problem is NP-hard in…
Given a digraph $G = (VG,AG)$, an \emph{even factor} $M \subseteq AG$ is a subset of arcs that decomposes into a collection of node-disjoint paths and even cycles. Even factors in digraphs were introduced by Geleen and Cunningham and…
We extend the definition of the Cartesian product to graphs with loops and show that the Sabidussi-Vizing unique factorization theorem for connected finite simple graphs still holds in this context for all connected finite graphs with at…
Let $F$ be a family of pseudo-disks in the plane, and $P$ be a finite subset of $F$. Consider the hypergraph $H(P,F)$ whose vertices are the pseudo-disks in $P$ and the edges are all subsets of $P$ of the form $\{D \in P \mid D \cap S \neq…
We aim to find orientations of mixed graphs optimizing the total reachability, a problem that has applications in causality and biology. For given a digraph $D$, we use $P(D)$ for the set of ordered pairs of distinct vertices in $V(D)$ and…
We present direct logarithmically optimal in theory and fast in practice algorithms to implement the tensor product high order finite element method on multi-dimensional rectangular parallelepipeds for solving PDEs of the Poisson kind. They…
The study of graph products is a major research topic and typically concerns the term $f(G*H)$, e.g., to show that $f(G*H)=f(G)f(H)$. In this paper, we study graph products in a non-standard form $f(R[G*H]$ where $R$ is a "reduction", a…
In this paper, we present exact exponential algorithms for computing branchwidth that are fast both in theory and in practice. The running times of these algorithms are single-exponential in the number of vertices. Our basic algorithm is…
Hypergraph width measures are a class of hypergraph invariants important in studying the complexity of constraint satisfaction problems (CSPs). We present a general exact exponential algorithm for a large variety of these measures. A…
We define a proportionally dense subgraph (PDS) as an induced subgraph of a graph with the property that each vertex in the PDS is adjacent to proportionally as many vertices in the subgraph as in the graph. We prove that the problem of…
We design fast deterministic algorithms for distance computation in the congested clique model. Our key contributions include: -- A $(2+\epsilon)$-approximation for all-pairs shortest paths in $O(\log^2{n} / \epsilon)$ rounds on unweighted…
In this paper, we begin the exploration of vertex-ordering problems through the lens of exponential-time approximation algorithms. In particular, we ask the following question: Can we simultaneously beat the running times of the fastest…
We investigate the complexity of several fundamental polynomial-time solvable problems on graphs and on matrices, when the given instance has low treewidth; in the case of matrices, we consider the treewidth of the graph formed by non-zero…
We consider the problem of finding a subgraph of a given graph minimizing the sum of given functions at vertices evaluated at their subgraph degrees. While the problem is NP-hard already for bipartite graphs when the functions are convex on…
We provide a deterministic algorithm that finds, in $\epsilon^{-O(1)} n^2$ time, an $\epsilon$-regular Frieze-Kannan partition of a graph on $n$ vertices. The algorithm outputs an approximation of a given graph as a weighted sum of…