Related papers: Simpler and Faster Directed Low-Diameter Decomposi…
In the decremental single-source shortest paths (SSSP) problem we want to maintain the distances between a given source node $s$ and every other node in an $n$-node $m$-edge graph $G$ undergoing edge deletions. While its static counterpart…
We consider the fundamental problem of constructing fast and small circuits for binary addition. We propose a new algorithm with running time $\mathcal O(n \log_2 n)$ for constructing linear-size $n$-bit adder circuits with a significantly…
We tackle the problems of computing the rightmost variant of the Lempel-Ziv factorizations in the online/sliding model. Previous best bounds for this problem are O(n log n) time with O(n) space, due to Amir et al. [IPL 2002] for the online…
In the classic Minimum Bisection problem we are given as input a graph $G$ and an integer $k$. The task is to determine whether there is a partition of $V(G)$ into two parts $A$ and $B$ such that $||A|-|B|| \leq 1$ and there are at most $k$…
We give an $\tilde{O}(n^{7/5} \log (nC))$-time algorithm to compute a minimum-cost maximum cardinality matching (optimal matching) in $K_h$-minor free graphs with $h=O(1)$ and integer edge weights having magnitude at most $C$. This improves…
We provide new tradeoffs between approximation and running time for the decremental all-pairs shortest paths (APSP) problem. For undirected graphs with $m$ edges and $n$ nodes undergoing edge deletions, we provide four new approximate…
We present faster algorithms for computing the 2-edge and 2-vertex strongly connected components of a directed graph, which are straightforward generalizations of strongly connected components. While in undirected graphs the 2-edge and…
The index coding problem is concerned with broadcasting encoded information to a collection of receivers in a way that enables each receiver to discover its required data based on its side information, which comprises the data required by…
We give faster algorithms for weak expander decompositions and approximate max flow on undirected graphs. First, we show that it is possible to "warm start" the cut-matching game when computing weak expander decompositions, avoiding the…
In the decremental Single-Source Shortest Path problem (SSSP), we are given a weighted directed graph $G=(V,E,w)$ undergoing edge deletions and a source vertex $r \in V$; let $n = |V|, m = |E|$ and $W$ be the aspect ratio of the graph. The…
We study the influence of a graph parameter called modular-width on the time complexity for optimally solving well-known polynomial problems such as Maximum Matching, Triangle Counting, and Maximum $s$-$t$ Vertex-Capacitated Flow. The…
We propose an algorithm with expected complexity of $\bigO(n\log n)$ arithmetic operations to solve a special shortest vector problem arising in computer-and-forward design, where $n$ is the dimension of the channel vector. This algorithm…
We develop new $(1+\epsilon)$-approximation algorithms for finding the global minimum edge-cut in a directed edge-weighted graph, and for finding the global minimum vertex-cut in a directed vertex-weighted graph. Our algorithms are…
We study two "above guarantee" versions of the classical Longest Path problem on undirected and directed graphs and obtain the following results. In the first variant of Longest Path that we study, called Longest Detour, the task is to…
We develop a framework for graph sparsification and sketching, based on a new tool, short cycle decomposition -- a decomposition of an unweighted graph into an edge-disjoint collection of short cycles, plus few extra edges. A simple…
A unit disk graph is the intersection graph of n congruent disks in the plane. Dominating sets in unit disk graphs are widely studied due to their application in wireless ad-hoc networks. Because the minimum dominating set problem for unit…
We study algorithmic and structural aspects of connectivity in hypergraphs. Given a hypergraph $H=(V,E)$ with $n = |V|$, $m = |E|$ and $p = \sum_{e \in E} |e|$ the best known algorithm to compute a global minimum cut in $H$ runs in time…
We show how to combine two techniques for efficiently computing shortest paths in directed planar graphs. The first is the linear-time shortest-path algorithm of Henzinger, Klein, Subramanian, and Rao [STOC'94]. The second is Fakcharoenphol…
We give the first O(m polylog(n)) time algorithms for approximating maximum flows in undirected graphs and constructing polylog(n) -quality cut-approximating hierarchical tree decompositions. Our algorithm invokes existing algorithms for…
We present a nearly-linear time algorithm for finding a minimum-cost flow in planar graphs with polynomially bounded integer costs and capacities. The previous fastest algorithm for this problem is based on interior point methods (IPMs) and…