Tree inclusion problems

Abstract

International audienceGiven two trees (a target T and a pattern P) and a natural number w, window embedded subtree problems consist in deciding whether P occurs as an embedded subtree of T and/or finding the number of size (at most) w windows of T which contain pattern P as an embedded subtree. P is an embedded subtree of T if P can be obtained by deleting some nodes from T (if a node v is deleted, all edges adjacent to v are also deleted, and outgoing edges are replaced by edges going from the parent of v (if it exists) to the children of v). Deciding whether P is an embedded subtree of T is known to be NP-complete. Our algorithms run in time O(|T|22|P|) where |T| (resp. |P|) is the size of T (resp. P)

Inclusion problems in trace monoids

“…Inclusion problems specific to trees were considered in [7][8][9][10]. Here, efficient algorithms for the solution of the problem on frequent episodes are proposed for various concepts of a window in trees.…”

Tree inclusions in windows and slices

“…In [CGM08] we solved related problems: deciding whether a pattern is an embedded subtree of a target within a w-window, counting the number of windows of height at most w of the target containing the pattern as an embedded subtree, and counting the number of occurrences of the pattern as an embedded subtree of the target within a window of height at most w. The algorithms in the present paper are of course inspired by the algorithms in [CGM08], to which Yu. Matiyasevich contributed in a fundamental way; the present paper is thus a natural complement to [CGM08].…”