Related papers: Local Routing on a Convex Polytope in R^3
We study the problem of optimal multi-robot path planning on graphs (MPP) over four distinct minimization objectives: the total arrival time, the makespan (last arrival time), the total distance, and the maximum (single-robot traveled)…
Let $s$ be a source point and $t$ be a destination point inside an $n$-vertex simple polygon $P$. Euclidean shortest paths and minimum-link paths between $s$ and $t$ inside $P$ have been well studied. Both these kinds of paths are simple…
We study the problem of planning paths for $p$ distinguishable pebbles (robots) residing on the vertices of an $n$-vertex connected graph with $p \le n$. A pebble may move from a vertex to an adjacent one in a time step provided that it…
This paper considers a natural fault-tolerant shortest paths problem: for some constant integer $f$, given a directed weighted graph with no negative cycles and two fixed vertices $s$ and $t$, compute (either explicitly or implicitly) for…
The packet routing problem asks to select routing paths that minimize the maximum edge congestion for a set of packets specified by source-destination vertex pairs. We revisit a semi-oblivious approach to this problem: each…
In the Distance-constrained Vehicle Routing Problem (DVRP), we are given a graph with integer edge weights, a depot, a set of $n$ terminals, and a distance constraint $D$. The goal is to find a minimum number of tours starting and ending at…
We study the replacement paths problem in the $\mathsf{CONGEST}$ model of distributed computing. Given an $s$-$t$ shortest path $P$, the goal is to compute, for every edge $e$ in $P$, the shortest-path distance from $s$ to $t$ avoiding $e$.…
Given two points in a simple polygon $P$ of $n$ vertices, its geodesic distance is the length of the shortest path that connects them among all paths that stay within $P$. The geodesic center of $P$ is the unique point in $P$ that minimizes…
The cut polytope ${\rm CUT}(n)$ is the convex hull of the cut vectors in a complete graph with vertex set $\{1,\ldots,n\}$. It is well known in the area of combinatorial optimization and recently has also been studied in a direct relation…
Hyperbolic tilings are natural infinite planar graphs where each vertex has degree $q$ and each face has $p$ edges for some $\frac1p+\frac1q<\frac12$. We study the structure of shortest paths in such graphs. We show that given a set of $n$…
We present several modifications to the previously proposed MSPP algorithm that can speed-up its execution considerably. The MSPP algorithm leverages a multiscale representation of the environment in $n$ dimensions. The information of the…
We propose a new speed and departure time optimization algorithm for the Pollution-Routing Problem (PRP), which runs in quadratic time and returns a certified optimal schedule. This algorithm is embedded into an iterated local search-based…
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…
In this paper, we present a new framework that exploits combinatorial optimization for efficiently generating a large variety of combinatorial objects based on graphs, matroids, posets and polytopes. Our method relies on a simple and…
Improving on the Voronoi cell based techniques of Micciancio and Voulgaris (SIAM J. Comp. 13), and Sommer, Feder and Shalvi (SIAM J. Disc. Math. 09), we give a Las Vegas $\tilde{O}(2^n)$ expected time and space algorithm for CVPP (the…
This paper introduces a new paradigm of optimal path planning, i.e., passage-traversing optimal path planning (PTOPP), that optimizes paths' traversed passages for specified optimization objectives. In particular, PTOPP is utilized to find…
The present paper is concerned with a recursive algorithm as a preprocessing step to find the convex hull of $n$ random points uniformly distributed in the plane. For such a set of points, it is shown that eliminating all but $O(\log n)$ of…
We consider a class of popular distributed non-convex optimization problems, in which agents connected by a network $\mathcal{G}$ collectively optimize a sum of smooth (possibly non-convex) local objective functions. We address the…
A roadmap for a semi-algebraic set $S$ is a curve which has a non-empty and connected intersection with all connected components of $S$. Hence, this kind of object, introduced by Canny, can be used to answer connectivity queries (with…
In the PATH COVER problem, one asks to cover the vertices of a graph using the smallest possible number of (not necessarily disjoint) paths. While the variant where the paths need to be pairwise vertex-disjoint, which we call PATH…