TY - GEN

T1 - Binary jumbled pattern matching on trees and tree-like structures

AU - Gagie, Travis

AU - Hermelin, Danny

AU - Landau, Gad M.

AU - Weimann, Oren

PY - 2013/9/24

Y1 - 2013/9/24

N2 - Binary jumbled pattern matching asks to preprocess a binary string S in order to answer queries (i,j) which ask for a substring of S that is of length i and has exactly j 1-bits. This problem naturally generalizes to vertex-labeled trees and graphs by replacing "substring" with "connected subgraph". In this paper, we give an O(n2 /log2 n)-time solution for trees, matching the currently best bound for (the simpler problem of) strings. We also give an O(g 2/3 n 4/3/(logn) 4/3)-time solution for strings that are compressed by a grammar of size g. This solution improves the known bounds when the string is compressible under many popular compression schemes. Finally, we prove that the problem is fixed-parameter tractable with respect to the treewidth w of the graph, even for a constant number of different vertex-labels, thus improving the previous best nO(w) algorithm.

AB - Binary jumbled pattern matching asks to preprocess a binary string S in order to answer queries (i,j) which ask for a substring of S that is of length i and has exactly j 1-bits. This problem naturally generalizes to vertex-labeled trees and graphs by replacing "substring" with "connected subgraph". In this paper, we give an O(n2 /log2 n)-time solution for trees, matching the currently best bound for (the simpler problem of) strings. We also give an O(g 2/3 n 4/3/(logn) 4/3)-time solution for strings that are compressed by a grammar of size g. This solution improves the known bounds when the string is compressible under many popular compression schemes. Finally, we prove that the problem is fixed-parameter tractable with respect to the treewidth w of the graph, even for a constant number of different vertex-labels, thus improving the previous best nO(w) algorithm.

UR - http://www.scopus.com/inward/record.url?scp=84884323652&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-40450-4_44

DO - 10.1007/978-3-642-40450-4_44

M3 - Conference contribution

AN - SCOPUS:84884323652

SN - 9783642404498

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 517

EP - 528

BT - Algorithms, ESA 2013 - 21st Annual European Symposium, Proceedings

T2 - 21st Annual European Symposium on Algorithms, ESA 2013

Y2 - 2 September 2013 through 4 September 2013

ER -