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We study the problem of finding the cycle of minimum cost-to-time ratio in a directed graph with $ n $ nodes and $ m $ edges. This problem has a long history in combinatorial optimization and has recently seen interesting applications in…
We provide an algorithm that, given an $n$-vertex $m$-edge Eulerian graph with polynomially bounded weights, computes an $\breve{O}(n\log^{2} n \cdot \varepsilon^{-2})$-edge $\varepsilon$-approximate Eulerian sparsifier with high…
Finding dense subgraphs is a fundamental problem with applications to community detection, clustering, and data mining. Our work focuses on finding approximate densest subgraphs in directed graphs in computational models for processing…
Let $P$ be a set of $n$ points in the plane, where each point $p\in P$ has a transmission radius $r(p)>0$. The transmission graph defined by $P$ and the given radii, denoted by $\mathcal{G}_{\mathrm{tr}}(P)$, is the directed graph whose…
In the Directed Feedback Vertex Set (DFVS) problem, the input is a directed graph $D$ on $n$ vertices and $m$ edges, and an integer $k$. The objective is to determine whether there exists a set of at most $k$ vertices intersecting every…
It is known that a better than $2$-approximation algorithm for the girth in dense directed unweighted graphs needs $n^{3-o(1)}$ time unless one uses fast matrix multiplication. Meanwhile, the best known approximation factor for a…
For an undirected unweighted graph G = (V, E) with n vertices and m edges, let d(u, v) denote the distance from u in V to v in V in G. An (alpha, beta)-stretch approximate distance oracle (ADO) for G is a data structure that, given u, v in…
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…
We consider the problem of approximating the girth, $g$, of an unweighted and undirected graph $G=(V,E)$ with $n$ nodes and $m$ edges. A seminal result of Itai and Rodeh [SICOMP'78] gave an additive $1$-approximation in $O(n^2)$ time, and…
While in many graph mining applications it is crucial to handle a stream of updates efficiently in terms of {\em both} time and space, not much was known about achieving such type of algorithm. In this paper we study this issue for a…
Consider the problem of maintaining source sink reachability($st$-Reachability), single source reachability(SSR) and strongly connected component(SCC) in an edge decremental directed graph. In particular, we design a randomized algorithm…
We devise new algorithms for the single-source shortest paths (SSSP) problem with non-negative edge weights in the CONGEST model of distributed computing. While close-to-optimal solutions, in terms of the number of rounds spent by the…
This paper presents a randomized algorithm for the problem of single-source shortest paths on directed graphs with real (both positive and negative) edge weights. Given an input graph with $n$ vertices and $m$ edges, the algorithm completes…
Given a directed graph $G = (V,E)$, undergoing an online sequence of edge deletions with $m$ edges in the initial version of $G$ and $n = |V|$, we consider the problem of maintaining all-pairs shortest paths (APSP) in $G$. Whilst this…
We present a labeling scheme that assigns labels of size $\tilde O(1)$ to the vertices of a directed weighted planar graph $G$, such that for any fixed $\varepsilon>0$ from the labels of any three vertices $s$, $t$ and $f$ one can determine…
We show how to compute for $n$-vertex planar graphs in $O(n^{11/6}{\rm polylog}(n))$ expected time the diameter and the sum of the pairwise distances. The algorithms work for directed graphs with real weights and no negative cycles. In…
The girth of a graph, i.e. the length of its shortest cycle, is a fundamental graph parameter. Unfortunately all known algorithms for computing, even approximately, the girth and girth-related structures in directed weighted $m$-edge and…
We consider the fundamental algorithmic problem of finding a cycle of minimum weight in a weighted graph. In particular, we show that the minimum weight cycle problem in an undirected n-node graph with edge weights in {1,...,M} or in a…
We study the central All-Pairs Shortest Paths (APSP) problem under the restriction that there are at most $d$ distinct weights on the outgoing edges from every node. For $d=n$ this is the classical (unrestricted) APSP problem that is…
The problem of finding multiple simple shortest paths in a weighted directed graph $G=(V,E)$ has many applications, and is considerably more difficult than the corresponding problem when cycles are allowed in the paths. Even for a single…