On Accuracy of Approximation for the Resource Constrained Shortest Path Problem

Shorter Path Constraints for the Resource Constrained Shortest Path Problem

Recently, new cost-based filtering algorithms for shorter-path constraints have been developed. However, so far only the theoretical properties of shorter-path constraint filtering have been studied. We provide the first extensive experimental evaluation of the new algorithms in the context of the resource constrained shortest path problem. We show how reasoning about path-substructures in comb...

Approximation Solutions for Time-Varying Shortest Path Problem

Abstract. Time-varying network optimization problems have tradition-ally been solved by specialized algorithms. These algorithms have NP-complement time complexity. This paper considers the time-varying short-est path problem, in which can be optimally solved in O(T(m + n)) time,where T is a given integer. For this problem with arbitrary waiting times,we propose an approximation algorithm, whic...

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Memory-Constrained Algorithms for Shortest Path Problem

We present an algorithm computing a shortest path between to vertices in a square grid graph with edge weights that uses memory less than linear in the number of vertices (apart from that for storing in the input). For any ε > 0, our algorithm uses a work space of O(n) words and runs in O(n) time.

Curve approximation and constrained shortest path problems

We study the following problem k-constrained shortest path problem: given an acyclic directed graph D = (V,E) with arc weights ci,j , (i, j) ∈ E, two nodes s and t and an integer k, nd a shortest st-path containing at most k arcs. An important application of the problem in linear curve approximation is discussed. Vertices and edges of associated polytopes are determined, and integrality of thes...