TY - GEN
T1 - Efficient all path score computations on grid graphs
AU - Matarazzo, Ury
AU - Tsur, Dekel
AU - Ziv-Ukelson, Michal
PY - 2013/9/24
Y1 - 2013/9/24
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/84884317502
U2 - 10.1007/978-3-642-38905-4_21
DO - 10.1007/978-3-642-38905-4_21
M3 - Conference contribution
AN - SCOPUS:84884317502
SN - 9783642389047
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 211
EP - 222
BT - Combinatorial Pattern Matching - 24th Annual Symposium, CPM 2013, Proceedings
T2 - 24th Annual Symposium on Combinatorial Pattern Matching, CPM 2013
Y2 - 17 June 2013 through 19 June 2013
ER -