Related papers: Improved Bounds for Shortest Paths in Dense Distan…
Given a graph $G=(V,E)$ and a set $T=\{ (s_i, t_i) : 1\leq i\leq k \}\subseteq V\times V$ of $k$ pairs, the $k$-vertex-disjoint-paths (resp. $k$-edge-disjoint-paths) problem asks to determine whether there exist~$k$ pairwise vertex-disjoint…
The dual of a planar graph $G$ is a planar graph $G^*$ that has a vertex for each face of $G$ and an edge for each pair of adjacent faces of $G$. The profound relationship between a planar graph and its dual has been the algorithmic basis…
In this paper, we propose new techniques for solving geometric optimization problems involving interpoint distances of a point set in the plane. Given a set $P$ of $n$ points in the plane and an integer $1 \leq k \leq \binom{n}{2}$, the…
Let $P$ be a path graph of $n$ vertices embedded in a metric space. We consider the problem of adding a new edge to $P$ to minimize the radius of the resulting graph. Previously, a similar problem for minimizing the diameter of the graph…
We study deterministic algorithms for computing graph cuts, with focus on two fundamental problems: balanced sparse cut and $k$-vertex connectivity for small $k$ ($k=O(\polylog n)$). Both problems can be solved in near-linear time with…
Let $G$ be a unit disk graph in the plane defined by $n$ disks whose positions are known. For the case when $G$ is unweighted, we give a simple algorithm to compute a shortest path tree from a given source in $O(n\log n)$ time. For the case…
In the Single Source Replacement Paths (SSRP) problem we are given a graph $G = (V, E)$, and a shortest paths tree $\widehat{K}$ rooted at a node $s$, and the goal is to output for every node $t \in V$ and for every edge $e$ in…
We examine the possibility of approximating Maximum Vertex-Disjoint Shortest Paths. In this problem, the input is an edge-weighted (directed or undirected) $n$-vertex graph $G$ along with $k$ terminal pairs…
The single-source shortest path problem is a classical problem in the research field of graph algorithm. In this paper, a new single-source shortest path algorithm for nonnegative weight graph is proposed. The algorithm can compress…
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…
We call a graph $G$ separable if a balanced separator can be computed for $G$ of size $O(n^c)$ with $c<1$. Many real-world graphs are separable such as graphs of bounded genus, graphs of constant treewidth, and graphs excluding a fixed…
We study the problem of computing approximate minimum edge cuts by distributed algorithms. We use a standard synchronous message passing model where in each round, $O(\log n)$ bits can be transmitted over each edge (a.k.a. the CONGEST…
In the dynamic Single-Source Shortest Paths (SSSP) problem, we are given a graph $G=(V,E)$ subject to edge insertions and deletions and a source vertex $s\in V$, and the goal is to maintain the distance $d(s,t)$ for all $t\in V$.…
The all-pairs shortest distances (APSD) with differential privacy (DP) problem takes as input an undirected, weighted graph $G = (V,E, \mathbf{w})$ and outputs a private estimate of the shortest distances in $G$ between all pairs of…
We propose an algorithm for solving the time-dependent shortest path problem in flow fields where the FIFO (first-in-first-out) assumption is violated. This problem variant is important for autonomous vehicles in the ocean, for example,…
A common way of partitioning graphs is through minimum cuts. One drawback of classical minimum cut methods is that they tend to produce small groups, which is why more balanced variants such as normalized and ratio cuts have seen more…
We initiate the study of approximation algorithms and computational barriers for constructing sparse $\alpha$-navigable graphs [IX23, DGM+24], a core primitive underlying recent advances in graph-based nearest neighbor search. Given an…
The all pairs shortest path problem (APSP) is one of the foundational problems in computer science. For weighted dense graphs on $n$ vertices, no truly sub-cubic algorithms exist to compute APSP exactly even for undirected graphs. This is…
In the age of real-time online traffic information and GPS-enabled devices, fastest-path computations between two points in a road network modeled as a directed graph, where each directed edge is weighted by a "travel time" value, are…
Images conveniently capture the result of physical processes, representing rich source of information for data driven medicine, engineering, and science. The modeling of an image as a graph allows the application of graph-based algorithms…