Related papers: A Simple 1.5-Approximation Algorithm for a Wide Ra…
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…
A spin system is a framework in which the vertices of a graph are assigned spins from a finite set. The interactions between neighbouring spins give rise to weights, so a spin assignment can also be viewed as a weighted graph homomorphism.…
In the distributed backup-placement problem each node of a network has to select one neighbor, such that the maximum number of nodes that make the same selection is minimized. This is a natural relaxation of the perfect matching problem, in…
We resolve the space complexity of linear sketches for approximating the maximum matching problem in dynamic graph streams where the stream may include both edge insertion and deletion. Specifically, we show that for any $\epsilon > 0$,…
Graphs naturally appear in several real-world contexts including social networks, the web network, and telecommunication networks. While the analysis and the understanding of graph structures have been a central area of study in algorithm…
We consider the {\em Capacitated Domination} problem, which models a service-requirement assignment scenario and is also a generalization of the well-known {\em Dominating Set} problem. In this problem, given a graph with three parameters…
It has become increasingly easy nowadays to collect approximate posterior samples via fast algorithms such as variational Bayes, but concerns exist about the estimation accuracy. It is tempting to build solutions that exploit approximate…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
For a graph formed by vertices and weighted edges, a generalized minimum dominating set (MDS) is a vertex set of smallest cardinality such that the summed weight of edges from each outside vertex to vertices in this set is equal to or…
We study the Dominating set problem and Independent Set Problem for dynamic graphs in the vertex-arrival model. We say that a dynamic algorithm for one of these problems is $k$-stable when it makes at most $k$ changes to its output…
In modern applications of graphs algorithms, where the graphs of interest are large and dynamic, it is unrealistic to assume that an input representation contains the full information of a graph being studied. Hence, it is desirable to use…
We present a general method of designing fast approximation algorithms for cut-based minimization problems in undirected graphs. In particular, we develop a technique that given any such problem that can be approximated quickly on trees,…
The locality of a graph problem is the smallest distance $T$ such that each node can choose its own part of the solution based on its radius-$T$ neighborhood. In many settings, a graph problem can be solved efficiently with a distributed or…
A dynamic graph algorithm is a data structure that answers queries about a property of the current graph while supporting graph modifications such as edge insertions and deletions. Prior work has shown strong conditional lower bounds for…
This paper addresses matrix approximation problems for matrices that are large, sparse and/or that are representations of large graphs. To tackle these problems, we consider algorithms that are based primarily on coarsening techniques,…
Graph summarization is beneficial in a wide range of applications, such as visualization, interactive and exploratory analysis, approximate query processing, reducing the on-disk storage footprint, and graph processing in modern hardware.…
Let G be a planar graph and F a set of additional edges not yet in G. The multiple edge insertion problem (MEI) asks for a drawing of G+F with the minimum number of pairwise edge crossings, such that the subdrawing of G is plane. Finding an…
We develop two adaptive discretization algorithms for convex semi-infinite optimization, which terminate after finitely many iterations at approximate solutions of arbitrary precision. In particular, they terminate at a feasible point of…
The Maximum Common Subgraph (MCS) problem plays a crucial role across various domains, bridging theoretical exploration and practical applications in fields like bioinformatics and social network analysis. Despite its wide applicability,…
The study of approximate matching in the Massively Parallel Computations (MPC) model has recently seen a burst of breakthroughs. Despite this progress, however, we still have a far more limited understanding of maximal matching which is one…