Related papers: Reconfiguring Shortest Paths in Graphs
Given a graph, the shortest-path problem requires finding a sequence of edges with minimum cumulative length that connects a source vertex to a target vertex. We consider a variant of this classical problem in which the position of each…
For a graph $G$ and $a,b\in V(G)$, the shortest path reconfiguration graph of $G$ with respect to $a$ and $b$ is denoted by $S(G,a,b)$. The vertex set of $S(G,a,b)$ is the set of all shortest paths between $a$ and $b$ in $G$. Two vertices…
The Shortest Path Reconfiguration problem has as input a graph G (with unit edge lengths) with vertices s and t, and two shortest st-paths P and Q. The question is whether there exists a sequence of shortest st-paths that starts with P and…
A rerouting sequence is a sequence of shortest st-paths such that consecutive paths differ in one vertex. We study the the Shortest Path Rerouting Problem, which asks, given two shortest st-paths P and Q in a graph G, whether a rerouting…
An st-shortest path, or st-path for short, in a graph G is a shortest (induced) path from s to t in G. Two st-paths are said to be adjacent if they differ on exactly one vertex. A reconfiguration sequence between two st-paths P and Q is a…
We study problems of reconfiguration of shortest paths in graphs. We prove that the shortest reconfiguration sequence can be exponential in the size of the graph and that it is NP-hard to compute the shortest reconfiguration sequence even…
We study reconfiguration problems for cliques in a graph, which determine whether there exists a sequence of cliques that transforms a given clique into another one in a step-by-step fashion. As one step of a transformation, we consider…
The shortest path problem is among the most fundamental combinatorial optimization problems to answer reachability queries. It is hard to deter-mine which vertices or edges are visited during shortest path traversals. In this paper, we…
A hypergraph is a set V of vertices and a set of non-empty subsets of V, called hyperedges. Unlike graphs, hypergraphs can capture higher-order interactions in social and communication networks that go beyond a simple union of pairwise…
For any graph $G$ with $a,b\in V(G)$, a shortest path reconfiguration graph can be formed with respect to $a$ and $b$; we denote such a graph as $S(G,a,b)$. The vertex set of $S(G,a,b)$ is the set of all shortest paths from $a$ to $b$ in…
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 search is based on the preliminary transformation of matrices or adjacency lists traditionally used in the study of graphs into projections cleared of redundant information (refined) followed by the selection of the desired shortest…
The problem of finding multiple simple shortest paths in a weighted directed graph $G=(V,E)$ has many applications, and is considerably more difficult than the corresponding problem when cycles are allowed in the paths. Even for a single…
This paper reviews the overview of the dynamic shortest path routing problem and the various neural networks to solve it. Different shortest path optimization problems can be solved by using various neural networks algorithms. The routing…
A shortest-path algorithm finds a path containing the minimal cost between two vertices in a graph. A plethora of shortest-path algorithms is studied in the literature that span across multiple disciplines. This paper presents a survey of…
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 $P_i$…
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.…
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…
The shortest path problem in graphs is a cornerstone of AI theory and applications. Existing algorithms generally ignore edge weight computation time. We present a generalized framework for weighted directed graphs, where edge weight can be…
In the k-Disjoint Shortest Paths problem, a set of terminal pairs of vertices $\{(s_i,t_i)\mid 1\le i\le k\}$ is given and we are asked to find paths $P_1,\ldots,P_k$ such that each path $P_i$ is a shortest path from $s_i$ to $t_i$ and…