Tree inclusions in windows and slices

Abstract

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. Given two trees (a target T and a pattern P) and a natural number w, we address two problems: 1. counting the number of windows of T having height exactly w and containing pattern P as an embedded subtree, and 2. counting the number of slices of T having height exactly w and containing pattern P as an embedded subtree.

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.…”

On trace inclusion optimization problems

“…These problems for sets of strings were considered by many authors [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. For the case of a fixed string, Baeza-Yates [4] has introduced the Directed Acyclic Subsequence Graph (DASG), i.e., the minimal partial automaton that is determined by this string and accepts the language of subsequences of this string.…”