Efficient all path score computations on grid graphs

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


We study the Integer-weighted Grid All Paths Scores (IGAPS) problem, which is given a grid graph, to compute the maximum weights of paths between every pair of a vertex on the first row of the graph and a vertex on the last row of the graph. We also consider a variant of this problem, periodic IGAPS, where the input grid graph is periodic and infinite. For these problems, we consider both the general (dense) and the sparse cases. For the sparse IGAPS problem with 0-1 weights, we give an O(r log3 (n2/r)) time algorithm, where r is the number of (diagonal) edges of weight 1. Our result improves upon the previous O(n√r) result by Krusche and Tiskin for this problem. For the periodic IGAPS problem we give an O(Cn2) time algorithm, where C is the maximum weight of an edge. This improves upon the previous O(C 2n2) algorithm of Tiskin. We also show a reduction from periodic IGAPS to IGAPS. This reduction yields o(n2) algorithms for this problem.

Original languageAmerican English
Title of host publicationCombinatorial Pattern Matching - 24th Annual Symposium, CPM 2013, Proceedings
Number of pages12
StatePublished - 24 Sep 2013
Event24th Annual Symposium on Combinatorial Pattern Matching, CPM 2013 - Bad Herrenalb, Germany
Duration: 17 Jun 201319 Jun 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7922 LNCS


Conference24th Annual Symposium on Combinatorial Pattern Matching, CPM 2013
CityBad Herrenalb

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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