Related papers: Arc-routing for winter road maintenance
Roughly speaking, gerrymandering is the systematic manipulation of the boundaries of electoral districts to make a specific (political) party win as many districts as possible. While typically studied from a geographical point of view,…
The Longest Path Problem is a question of finding the maximum length between pairs of vertices of a graph. In the general case, the problem is NP-complete. However, there is a small collection of graph classes for which there exists an…
We study the problem of learning a node-labeled tree given independent traces from an appropriately defined deletion channel. This problem, tree trace reconstruction, generalizes string trace reconstruction, which corresponds to the tree…
The problem of providing meaningful routing directions over road networks is of great importance. In many real-life cases, the fastest route may not be the ideal choice for providing directions in written, spoken text, or for an unfamiliar…
In this paper we study the routing and rebalancing problem for a fleet of autonomous vehicles providing on-demand transportation within a congested urban road network (that is, a road network where traffic speed depends on vehicle density).…
Automated driving in urban scenarios requires efficient planning algorithms able to handle complex situations in real-time. A popular approach is to use graph-based planning methods in order to obtain a rough trajectory which is…
This paper studies the fundamental problem of how to reroute $k$ unsplittable flows of a certain demand in a capacitated network from their current paths to their respective new paths, in a congestion-free manner and fast. This scheduling…
We study the computational complexity of optimally solving multi-robot path planning problems on planar graphs. For four common time- and distance-based objectives, we show that the associated path optimization problems for multiple robots…
Mathematical modeling is a standard approach to solve many real-world problems and {\em diversity} of solutions is an important issue, emerging in applying solutions obtained from mathematical models to real-world problems. Many studies…
We consider a routing problem which plays an important role in several applications, primarily in communication network planning and VLSI layout design. The original underlying graph algorithmic task is called Disjoint Paths problem. In…
Given a graph, the sparsest cut problem asks for a subset of vertices whose edge expansion (the normalized cut given by the subset) is minimized. In this paper, we study a generalization of this problem seeking for $ k $ disjoint subsets of…
This paper deals with the Stochastic Capacitated Arc Routing Problem (SCARP), obtained by randomizing quantities on the arcs in the CARP. Optimization problems for the SCARP are characterized by decisions that are made without knowing their…
The quadratic shortest path problem is the problem of finding a path in a directed graph such that the sum of interaction costs over all pairs of arcs on the path is minimized. We derive several semidefinite programming relaxations for the…
Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…
The {\it partially disjoint paths problem} is: {\it given:} a directed graph, vertices $r_1,s_1,\ldots,r_k,s_k$, and a set $F$ of pairs $\{i,j\}$ from $\{1,\ldots,k\}$, {\it find:} for each $i=1,\ldots,k$ a directed $r_i-s_i$ path $P_i$…
Given a digraph $D=(V,A)$ and a positive integer $k$, an arc set $F\subseteq A$ is called a \textbf{$k$-arborescence} if it is the disjoint union of $k$ spanning arborescences. The problem of finding a minimum cost $k$-arborescence is known…
Temporal dependencies between customer visits, such as synchronization constraints, pose a fundamental challenge in vehicle routing. These dependencies, which arise in applications such as home healthcare routing, aircraft scheduling, and…
Expanders are powerful algorithmic structures with two key properties: they are a) routable: for any multi-commodity flow unit demand, there exists a routing with low congestion over short paths, where a demand is unit if the amount of…
We show two results related to the Hamiltonicity and $k$-Path algorithms in undirected graphs by Bj\"orklund [FOCS'10], and Bj\"orklund et al., [arXiv'10]. First, we demonstrate that the technique used can be generalized to finding some…
This paper deals with a multi-period extension of the p-center problem, in which arc traversal times vary over time, and facilities are mobile units that can be relocated multiple times during the planning horizon. The problem arises in…