Related papers: A reduction of the logspace shortest path problem …
A linear-time algorithm for generating auxiliary subgraphs for the 3-edge-connected components of a connected multigraph is presented. The algorithm uses an innovative graph contraction operation and makes only one pass over the graph. By…
Let G be a graph embedded on a surface of genus g with b boundary cycles. We describe algorithms to compute multiple types of non-trivial cycles in G, using different techniques depending on whether or not G is an undirected graph. If G is…
We formulate and study the thinnest path problem in wireless ad hoc networks. The objective is to find a path from a source to its destination that results in the minimum number of nodes overhearing the message by a judicious choice of…
We give O(log^2 n)-approximation algorithm based on the cut-matching framework of [10, 13, 14] for computing the sparsest cut on directed graphs. Our algorithm uses only O(log^2 n) single commodity max-flow computations and thus breaks the…
Given an undirected $n$-vertex graph and $k$ pairs of terminal vertices $(s_1,t_1), \ldots, (s_k,t_k)$, the $k$-Disjoint Shortest Paths ($k$-DSP)-problem asks whether there are $k$ pairwise vertex-disjoint paths $P_1,\ldots, P_k$ such that…
In this paper, we revisit the classic approximate All-Pairs Shortest Paths (APSP) problem in undirected graphs. For unweighted graphs, we provide an algorithm for $2$-approximate APSP in $\tilde O(n^{2.5-r}+n^{\omega(r)})$ time, for any…
An instance of the Connected Maximum Cut problem consists of an undirected graph G = (V, E) and the goal is to find a subset of vertices S $\subseteq$ V that maximizes the number of edges in the cut \delta(S) such that the induced graph…
We consider approximate {\em path-reporting} distance oracles, distance labeling and labeled routing with extremely low space requirement, for general undirected graphs. For distance oracles, we show how to break the n\log n space bound of…
We consider the all pairs all shortest paths (APASP) problem, which maintains the shortest path dag rooted at every vertex in a directed graph G=(V,E) with positive edge weights. For this problem we present a decremental algorithm (that…
The paper focuses on two problems: (i) how to orient the edges of an undirected graph in order to maximize the number of ordered vertex pairs (x,y) such that there is a directed path from x to y, and (ii) how to orient the edges so as to…
In this paper I present general outlook on questions relevant to the basic graph algorithms; Finding the Shortest Path with Positive Weights and Minimum Spanning Tree. I will show so far known solution set of basic graph problems and…
This paper investigates the complexity of finding secluded paths in graphs. We focus on the \textsc{Short Secluded Path} problem and a natural new variant we introduce, \textsc{Shortest Secluded Path}. Formally, given an undirected graph…
We consider the unrestricted, minimal, and bounded representation problems for unit interval (UIG) and unit circular-arc (UCA) graphs. In the unrestricted version, a proper circular-arc (PCA) model $\cal M$ is given and the goal is to…
We study the design of fixed-parameter algorithms for problems already known to be solvable in polynomial time. The main motivation is to get more efficient algorithms for problems with unattractive polynomial running times. Here, we focus…
In this paper we present the first deterministic polynomial time algorithm for determining the existence of a Hamiltonian cycle and finding a Hamiltonian cycle in general graphs. Our algorithm can also solve the Hamiltonian path problem in…
This study addresses optimal rake-link formation in large-scale timetabled rail operations by modeling the problem as a directed acyclic graph and solving it via the minimum path cover algorithm. It enables efficient rake-to-service…
Graph isomorphism problem is a known hard problem. In this paper, a novel randomized algorithm is proposed for this problem which is very simple and fast. It solves the graph isomorphism problem with running time O(n^2.373) for any pair of…
The problem of finding the shortest path in a graph G(V, E) has been widely studied. However, in many applications it is necessary to compute an arbitrary number of them, k. Even though the problem has raised a lot of interest from…
We consider the problem of computing all-pairs shortest paths in a directed graph with real weights assigned to vertices. For an $n\times n$ 0-1 matrix $C,$ let $K_{C}$ be the complete weighted graph on the rows of $C$ where the weight of…
Level-sensitive latches are widely used in high- performance designs. For such circuits efficient statistical timing analysis algorithms are needed to take increasing process vari- ations into account. But existing methods solving this…