Related papers: Into the Square - On the Complexity of Quadratic-T…
Let $G$ be a directed graph with $n$ vertices and $m$ edges, embedded on a surface $S$, possibly with boundary, with first Betti number $\beta$. We consider the complexity of finding closed directed walks in $G$ that are either contractible…
We address the problem of testing whether a given dynamic graph is temporally connected, {\it i.e} a temporal path (also called a {\em journey}) exists between all pairs of vertices. We consider a discrete version of the problem, where the…
Consider a directed or an undirected graph with integral edge weights from the set [-W, W], that does not contain negative weight cycles. In this paper, we introduce a general framework for solving problems on such graphs using matrix…
We consider the classical Minimum Balanced Cut problem: given a graph $G$, compute a partition of its vertices into two subsets of roughly equal volume, while minimizing the number of edges connecting the subsets. We present the first {\em…
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…
We experimentally evaluate the practical state-of-the-art in graph bipartization (Odd Cycle Transversal), motivated by recent advances in near-term quantum computing hardware and the related embedding problems. We assemble a preprocessing…
We study the computational complexity of approximately computing the partition function of a spin system. Techniques based on standard counting-to-sampling reductions yield $\tilde{O}(n^2)$-time algorithms, where $n$ is the size of the…
Given a directed graph $G$, a transitive reduction $G^t$ of $G$ (first studied by Aho, Garey, Ullman [SICOMP `72]) is a minimal subgraph of $G$ that preserves the reachability relation between every two vertices in $G$. In this paper, we…
We consider the distributed message-passing {LOCAL} model. In this model a communication network is represented by a graph where vertices host processors, and communication is performed over the edges. Computation proceeds in synchronous…
There have been several algorithms designed to optimise matrix multiplication. From schoolbook method with complexity $O(n^3)$ to advanced tensor-based tools with time complexity $O(n^{2.3728639})$ (lowest possible bound achieved), a lot of…
We revisit a classical graph-theoretic problem, the \textit{single-source shortest-path} (SSSP) problem, in weighted unit-disk graphs. We first propose an exact (and deterministic) algorithm which solves the problem in $O(n \log^2 n)$ time…
In the $k$-cut problem, we are given an edge-weighted graph $G$ and an integer $k$, and have to remove a set of edges with minimum total weight so that $G$ has at least $k$ connected components. The current best algorithms are an…
We improve the running time of the general algorithmic technique known as Baker's approach (1994) on H-minor-free graphs from O(n^{f(|H|)}) to O(f(|H|) n^{O(1)}). The numerous applications include e.g. a 2-approximation for coloring and…
The Strong Exponential Time Hypothesis and the OV-conjecture are two popular hardness assumptions used to prove a plethora of lower bounds, especially in the realm of polynomial-time algorithms. The OV-conjecture in moderate dimension…
We initiate the study of combinatorial algorithms for Triangle Detection in $H$-free graphs. The goal is to decide if a graph that forbids a fixed pattern $H$ as a subgraph contains a triangle, using only "combinatorial" methods that…
In this paper, we present two main results. First, by only one conjecture (Conjecture 2.9) for recognizing a vertex symmetric graph, which is the hardest task for our problem, we construct an algorithm for finding an isomorphism between two…
Algorithms which compute properties over graphs have always been of interest in computer science, with some of the fundamental algorithms, such as Dijkstra's algorithm, dating back to the 50s. Since the 70s there as been interest in…
Consider the following distance query for an $n$-node graph $G$ undergoing edge insertions and deletions: given two sets of nodes $I$ and $J$, return the distances between every pair of nodes in $I\times J$. This query is rather general and…
A graph $G$ is contractible to a graph $H$ if there is a set $X \subseteq E(G)$, such that $G/X$ is isomorphic to $H$. Here, $G/X$ is the graph obtained from $G$ by contracting all the edges in $X$. For a family of graphs $\cal F$, the…
Many hard graph problems, such as Hamiltonian Cycle, become FPT when parameterized by treewidth, a parameter that is bounded only on sparse graphs. When parameterized by the more general parameter clique-width, Hamiltonian Cycle becomes…