相关论文: Rerouting shortest paths in planar graphs

The $k$ disjoint shortest paths problem ($k$-DSPP) on a graph with $k$ source-sink pairs $(s_i, t_i)$ asks for the existence of $k$ pairwise edge- or vertex-disjoint shortest $s_i$-$t_i$-paths. It is known to be NP-complete if $k$ is part…

The purpose of this work is to introduce and characterize the Bounded Acceleration Shortest Path (BASP) problem, a generalization of the Shortest Path (SP) problem. This problem is associated to a graph: the nodes represent positions of a…

We study the computational complexity of routing multiple objects through a network in such a way that only few collisions occur: Given a graph $G$ with two distinct terminal vertices and two positive integers $p$ and $k$, the question is…

Given an edge-weighted undirected graph and a list of k source-sink pairs of vertices, the well-known minimum multicut problem consists in selecting a minimum-weight set of edges whose removal leaves no path between every source and its…

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…

Given a graph $G$, and terminal vertices $s$ and $t$, the TRACKING PATHS problem asks to compute a minimum number of vertices to be marked as trackers, such that the sequence of trackers encountered in each s-t path is unique. TRACKING…

Given a directed graph of nodes and edges connecting them, a common problem is to find the shortest path between any two nodes. Here we show that the shortest path distances can be found by a simple matrix inversion: If the edges are given…

We show that the following variation of the single-source shortest path problem is NP-complete. Let a weighted, directed, acyclic graph $G=(V,E,w)$ with source and sink vertices $s$ and $t$ be given. Let in addition a mapping $f$ on $E$ be…

A pangenome captures the genetic diversity across multiple individuals simultaneously, providing a more comprehensive reference for genome analysis than a single linear genome, which may introduce allele bias. A widely adopted pangenome…

We introduce in a general setting a dynamic programming method for solving reconfiguration problems. Our method is based on contracted solution graphs, which are obtained from solution graphs by performing an appropriate series of edge…

We study the following Two-Sets Cut-Uncut problem on planar graphs. Therein, one is given an undirected planar graph $G$ and two sets of vertices $S$ and $T$. The question is, what is the minimum number of edges to remove from $G$, such…

The problems of Permutation Routing via Matching and Token Swapping are reconfiguration problems on graphs. This paper is concerned with the complexity of those problems and a colored variant. For a given graph where each vertex has a…

Motivated by the fact that in a space where shortest paths are unique, no two shortest paths meet twice, we study a question posed by Greg Bodwin: Given a geodetic graph $G$, i.e., an unweighted graph in which the shortest path between any…

In the recent research of data mining, frequent structures in a sequence of graphs have been studied intensively, and one of the main concern is changing structures along a sequence of graphs that can capture dynamic properties of data. On…

Given a planar graph G on n vertices and an integer parameter r<n, an r-division of G with few holes is a decomposition of G into O(n/r) regions of size at most r such that each region contains at most a constant number of faces that are…

In this work, we follow the current trend on temporal graph realization, where one is given a property P and the goal is to determine whether there is a temporal graph, that is, a graph where the edge set changes over time, with property P…

In this paper we present some new complexity results on the routing time of a graph under the \textit{routing via matching} model. This is a parallel routing model which was introduced by Alon et al\cite{alon1994routing}. The model can be…

A minimum path cover (MPC) of a directed acyclic graph (DAG) $G = (V,E)$ is a minimum-size set of paths that together cover all the vertices of the DAG. Computing an MPC is a basic polynomial problem, dating back to Dilworth's and…

We investigate the problem of computing a minimum set of solutions that approximates within a specified accuracy $\epsilon$ the Pareto curve of a multiobjective optimization problem. We show that for a broad class of bi-objective problems…

Let G be a directed graph with n vertices and non-negative weights in its directed edges, embedded on a surface of genus g, and let f be an arbitrary face of G. We describe a randomized algorithm to preprocess the graph in O(gn log n) time…