Related papers: FPT Approximation and Subexponential Algorithms fo…

We study the complexity of approximating the vertex expansion of graphs $G = (V,E)$, defined as \[ \Phi^V := \min_{S \subset V} n \cdot \frac{|N(S)|}{|S| |V \backslash S|}. \] We give a simple polynomial-time algorithm for finding a subset…

Given a fixed positive integer $k$ and a simple undirected graph $G = (V, E)$, the {\em $k^-$-path partition} problem, denoted by $k$PP for short, aims to find a minimum collection $\cal{P}$ of vertex-disjoint paths in $G$ such that each…

The \emph{maximal $k$-edge-connected subgraphs} problem is a classical graph clustering problem studied since the 70's. Surprisingly, no non-trivial technique for this problem in weighted graphs is known: a very straightforward…

Two kinds of approximation algorithms exist for the k-BALANCED PARTITIONING problem: those that are fast but compute unsatisfying approximation ratios, and those that guarantee high quality ratios but are slow. In this paper we prove that…

We study the classic Max-Cut problem under multiple cardinality constraints, which we refer to as the Constrained Max-Cut problem. Given a graph $G=(V, E)$, a partition of the vertices into $c$ disjoint parts $V_1, \ldots, V_c$, and…

Edge-Geodetic Sets play a crucial role in network monitoring and optimization, wherein the goal is to strategically place monitoring stations on vertices of a network, represented as a graph, to ensure complete coverage of edges and…

We study two related problems: finding a set of k vertices and minimum number of edges (kmin) and finding a graph with at least m' edges and minimum number of vertices (mvms). Goldschmidt and Hochbaum \cite{GH97} show that the mvms problem…

We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…

A graph $G$ is called B$_k$-VPG (resp., B$_k$-EPG), for some constant $k\geq 0$, if it has a string representation on a grid such that each vertex is an orthogonal path with at most $k$ bends and two vertices are adjacent in $G$ if and only…

We pursue a study of the Generalized Demand Matching problem, a common generalization of the $b$-Matching and Knapsack problems. Here, we are given a graph with vertex capacities, edge profits, and asymmetric demands on the edges. The goal…

The input to the Multiway Cut problem is a weighted undirected graph, with nonnegative edge weights, and $k$ designated terminals. The goal is to partition the vertices of the graph into $k$ parts, each containing exactly one of the…

In this paper, we introduce the problem of Matroid-Constrained Vertex Cover: given a graph with weights on the edges and a matroid imposed on the vertices, our problem is to choose a subset of vertices that is independent in the matroid,…

We study the problem of graph clustering where the goal is to partition a graph into clusters, i.e. disjoint subsets of vertices, such that each cluster is well connected internally while sparsely connected to the rest of the graph. In…

We consider the question of orienting the edges in a graph $G$ such that every vertex has bounded out-degree. For graphs of arboricity $\alpha$, there is an orientation in which every vertex has out-degree at most $\alpha$ and, moreover,…

Given a list of k source-sink pairs in an edge-weighted graph G, the minimum multicut problem consists in selecting a set of edges of minimum total weight in G, such that removing these edges leaves no path from each source to its…

Graph Crossing Number is a fundamental problem with various applications. In this problem, the goal is to draw an input graph $G$ in the plane so as to minimize the number of crossings between the images of its edges. Despite extensive…

In this paper, we propose and study a new semi-random model for graph partitioning problems. We believe that it captures many properties of real--world instances. The model is more flexible than the semi-random model of Feige and Kilian and…

The graph homomorphism problem (HOM) asks whether the vertices of a given $n$-vertex graph $G$ can be mapped to the vertices of a given $h$-vertex graph $H$ such that each edge of $G$ is mapped to an edge of $H$. The problem generalizes the…

We consider the capacitated domination problem, which models a service-requirement assigning scenario and which is also a generalization of the dominating set problem. In this problem, we are given a graph with three parameters defined on…

We show that graphs excluding $K_{2,t}$ as a minor admit a $f(t)$-round $50$-approximation deterministic distributed algorithm for Minimum Dominating Set. The result extends to Minimum Vertex Cover. Though fast and approximate distributed…