Related papers: Shortest path problem in rectangular complexes of …
We initiate the study of the shortest reconfiguration problem for independent sets under the adjacency relation derived from the independent set polytope. Given a graph and two independent sets, the problem asks for a shortest sequence…
The problem of finding a path between two points while avoiding obstacles is critical in robotic path planning. We focus on the feasibility problem: determining whether such a path exists. We model the robot as a query-specific rectangular…
Let S be a subdivision of the plane into polygonal regions, where each region has an associated positive weight. The weighted region shortest path problem is to determine a shortest path in S between two points s, t in R^2, where the…
Consider the continuum of points along the edges of a network, i.e., a connected, undirected graph with positive edge weights. We measure the distance between these points in terms of the weighted shortest path distance, called the network…
We study the knapsack problem with graph theoretic constraints. That is, we assume that there exists a graph structure on the set of items of knapsack and the solution also needs to satisfy certain graph theoretic properties on top of…
We consider two orientation problems in a graph, namely the minimization of the sum of all the shortest path lengths and the minimization of the diameter. We show that it is NP-complete to decide whether a graph has an orientation such that…
We study SINGLE-SOURCE SHORTEST PATH (SSSP) on unweighted intersection graphs whose node set corresponds to a set of $n$ constant-complexity objects in the plane. We prove SSSP can be solved in $O(U(n)\ \mathrm{polylog}\,n)$ expected time…
Given an undirected graph and two disjoint vertex pairs $s_1,t_1$ and $s_2,t_2$, the Shortest two disjoint paths problem (S2DP) asks for the minimum total length of two vertex disjoint paths connecting $s_1$ with $t_1$, and $s_2$ with…
We consider the standard message passing model; we assume the system is fully synchronous: all processes start at the same time and time proceeds in synchronised rounds. In each round each vertex can transmit a different message of size…
We present an $O(nm)$ algorithm for all-pairs shortest paths computations in a directed graph with $n$ nodes, $m$ arcs, and nonnegative integer arc costs. This matches the complexity bound attained by Thorup \cite{Thorup1999} for the…
The approximate single-source shortest-path problem is as follows: given a graph with nonnegative edge weights and a designated source vertex $s$, return estimates of the distances from~$s$ to each other vertex such that the estimate falls…
In this paper we introduce a new algorithm for the \emph{$k$-Shortest Simple Paths} (\kspp{k}) problem with an asymptotic running time matching the state of the art from the literature. It is based on a black-box algorithm due to…
We show that the shadow vertex algorithm can be used to compute a short path between a given pair of vertices of a polytope P = {x : Ax \leq b} along the edges of P, where A \in R^{m \times n} is a real-valued matrix. Both, the length of…
We present fast algorithms for approximate shortest paths in the massively parallel computation (MPC) model. We provide randomized algorithms that take $poly(\log{\log{n}})$ rounds in the near-linear memory MPC model. Our results are for…
Dijkstra's algorithm is the standard method for computing shortest paths on arbitrary graphs. However, it is slow for large graphs, taking at least linear time. It has been long known that for real world road networks, creating a hierarchy…
Given an undirected graph $G=(V,E)$, vertices $s,t\in V$, and an integer $k$, Tracking Shortest Paths requires deciding whether there exists a set of $k$ vertices $T\subseteq V$ such that for any two distinct shortest paths between $s$ and…
We present parallel algorithms for computing single-source reachability and shortest paths on directed $n$-vertex $m$-edge graphs using near-linear $\tilde{O}(m)$ work and $o(\sqrt{n})$ depth whenever $m\ge n^{1+o(1)}$. At the extreme of…
Matrix $M$ is {\em $k$-concise} if the finite entries of each column of $M$ consist of $k$ or less intervals of identical numbers. We give an $O(n+m)$-time algorithm to compute the row minima of any $O(1)$-concise $n\times m$ matrix. Our…
We present a general technique, based on parametric search with some twist, for solving a variety of optimization problems on a set of semi-algebraic geometric objects of constant complexity. The common feature of these problems is that…
Let $\kappa(s,t)$ denote the maximum number of internally disjoint $st$-paths in an undirected graph $G$. We consider designing a compact data structure that answers $k$-bounded node connectivity queries: given $s,t \in V$ return…