Counting Approximately-Shortest Paths in Directed Acyclic Graphs

Matús Mihalák, Rastislav Šrámek, Peter Widmayer

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review

Abstract

Given a directed acyclic graph with positive edge-weights, two vertices s and t, and a threshold-weight l, we present a fully-polynomial time approximation-scheme for the problem of counting the s-t paths of length at most l. We extend the algorithm for the case of two (or more) instances of the same problem. That is, given two graphs that have the same vertices and edges and differ only in edge-weights, and given two threshold-weights l 1 and l 2, we show how to approximately count the s-t paths that have length at most l 1 in the first graph and length not much larger than l 2 in the second graph. We believe that our algorithms should find application in counting approximate solutions of related optimization problems, where finding an (optimum) solution can be reduced to the computation of a shortest path in a purpose-built auxiliary graph.
Original languageEnglish
Title of host publicationProc. 11th International Workshop on Approximation and Online Algorithms (WAOA)
PublisherSpringer Verlag
Pages156-167
Number of pages12
DOIs
Publication statusPublished - 2013

Publication series

SeriesLecture Notes in Computer Science
Volume8447

Cite this

Mihalák, M., Šrámek, R., & Widmayer, P. (2013). Counting Approximately-Shortest Paths in Directed Acyclic Graphs. In Proc. 11th International Workshop on Approximation and Online Algorithms (WAOA) (pp. 156-167). Springer Verlag. Lecture Notes in Computer Science, Vol.. 8447 https://doi.org/10.1007/978-3-319-08001-7_14