Computational issues in exploiting dependent and-parallelism in logic programming: leftness detection in dynamic search trees

Authors:
Yao Wu;Enrico Pontelli;Desh Ranjan
Affiliations:
Department of Computer Science, New Mexico State University;Department of Computer Science, New Mexico State University;Department of Computer Science, New Mexico State University
Venue:
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Year:
2005

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Abstract

We present efficient Pure Pointer Machine (PPM) algorithms to test for “leftness” in dynamic search trees and related problems. In particular, we show that the problem of testing if a node x is in the leftmost branch of the subtree rooted in node y, in a dynamic tree that grows and shrinks at the leaves, can be solved on PPMs in worst-case O((lg lg n)2) time per operation in the semi-dynamic case—i.e.,all the operations that add leaves to the tree are performed before any other operations—where n is the number of operations that affect the structure of the tree. We also show that the problem can be solved on PPMs in amortized O((lg lg n)2) time per operation in the fully dynamic case.