Related papers: Constrained Routing Between Non-Visible Vertices
The Constraint Shortest Path (CSP) problem is as follows. An $n$-vertex graph is given, each edge/arc assigned two weights. Let us call them "cost" and "length" for definiteness. Finding a min-cost upper-bounded length path between a given…
This paper presents near-optimal deterministic parallel and distributed algorithms for computing $(1+\varepsilon)$-approximate single-source shortest paths in any undirected weighted graph. On a high level, we deterministically reduce this…
The application of learning based methods to vehicle routing problems has emerged as a pivotal area of research in combinatorial optimization. These problems are characterized by vast solution spaces and intricate constraints, making…
Recently, several studies have explored the use of neural network to solve different routing problems, which is an auspicious direction. These studies usually design an encoder-decoder based framework that uses encoder embeddings of nodes…
Graph embedding is a fundamental problem of mapping nodes of a guest graph into a host graph while minimizing the distance distortion, with broad applications, including virtual network embeddings into physical topologies, VLSI design, or…
In the Disjoint Shortest Paths problem one is given a graph $G$ and a set $\mathcal{T}=\{(s_1,t_1),\dots,(s_k,t_k)\}$ of $k$ vertex pairs. The question is whether there exist vertex-disjoint paths $P_1,\dots,P_k$ in $G$ so that each $P_i$…
We present a distributed self-adjusting algorithm for skip graphs that minimizes the average routing costs between arbitrary communication pairs by performing topological adaptation to the communication pattern. Our algorithm is fully…
We consider the ideal orientation problem in planar graphs. In this problem, we are given an undirected graph $G$ with positive edge lengths and $k$ pairs of distinct vertices $(s_1, t_1), \dots, (s_k, t_k)$ called terminals, and we want to…
Modern computer networks support interesting new routing models in which traffic flows from a source s to a destination t can be flexibly steered through a sequence of waypoints, such as (hardware) middleboxes or (virtualized) network…
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…
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…
In this paper, we consider the problem of exploring unknown environments with autonomous agents. We model the environment as a graph with edge weights and analyze the task of visiting all vertices of the graph at least once. The hardness of…
Computing a shortest path between two nodes in an undirected unweighted graph is among the most basic algorithmic tasks. Breadth first search solves this problem in linear time, which is clearly also a lower bound in the worst case.…
Given in the plane a set $S$ of $n$ points and a set of disks centered at these points, the disk graph $G(S)$ induced by these disks has vertex set $S$ and an edge between two vertices if their disks intersect. Note that the disks may have…
We consider the following online optimization problem. We are given a graph $G$ and each vertex of the graph is assigned to one of $\ell$ servers, where servers have capacity $k$ and we assume that the graph has $\ell \cdot k$ vertices.…
Given a distributed network represented by a weighted undirected graph $G=(V,E)$ on $n$ vertices, and a parameter $k$, we devise a distributed algorithm that computes a routing scheme in $(n^{1/2+1/k}+D)\cdot n^{o(1)}$ rounds, where $D$ is…
We consider the task of drawing a graph on multiple horizontal layers, where each node is assigned a layer, and each edge connects nodes of different layers. Known algorithms determine the orders of nodes on each layer to minimize crossings…
In this article, we present a construction of a spanner on a set of $n$ points in $\mathbf{R}^d$ that we call a heavy path WSPD spanner. The construction is parameterized by a constant $s > 2$ called the separation ratio. The size of the…
In robotics, coordinating a group of robots is an essential task. This work presents the communication-constrained multi-agent multi-goal path planning problem and proposes a graph-search based algorithm to address this task. Given a fleet…
Read-only memory model is a classical model of computation to study time-space tradeoffs of algorithms. One of the classical results on the ROM model is that any sorting algorithm that uses O(s) words of extra space requires $\Omega…