Finding a Shortest Non-Zero Path in Group-Labeled Graphs

Finding a Path in Group-Labeled Graphs with Two Labels Forbidden

The parity of the length of paths and cycles is a classical and well-studied topic in graph theory and theoretical computer science. The parity constraints can be extended to the label constraints in a group-labeled graph, which is a directed graph with a group label on each arc. Recently, paths and cycles in group-labeled graphs have been investigated, such as finding non-zero disjoint paths a...

Two optimal algorithms for finding bi-directional shortest path design problem in a block layout

In this paper, Shortest Path Design Problem (SPDP) in which the path is incident to all cells is considered. The bi-directional path is one of the known types of configuration of networks for Automated Guided Vehi-cles (AGV).To solve this problem, two algorithms are developed. For each algorithm an Integer Linear Pro-gramming (ILP) is determined. The objective functions of both algorithms are t...

Packing non-zero A-paths in an undirected model of group labeled graphs

Let Γ be an abelian group, and let γ : E(G) → Γ be be a function assigning values in Γ to every edge of a graph G. For a subgraph H of G, let γ(H) = ∑ e∈E(H) γ(e). In this article, we show that there exists a function f(k) such that the following holds. For a set A of vertices of G, an A-path is a path with both endpoints in A and otherwise disjoint from A. Then either there exist k vertex disj...

An Algorithm for Packing Non-zero A-paths in Group-labeled Graphs

FATES: Finding A Time dEpendent Shortest path

We model a moving object as a sizable physical entity equipped with GPS, wireless communication capability, and a computer. Based on a grid model, we develop a distributed system, FATES, to manage data for moving objects in a two-dimensional space. The system is used to provide time-dependent shortest paths for moving objects. The performance study shows that FATES yields shorter average trip t...