Searching in dynamic tree-like partial orders

Authors:
Brent Heeringa;Marius Cătălin Iordan;Louis Theran
Affiliations:
Dept. of Computer Science, Williams College;Dept. of Computer Science, Stanford University;Dept. of Mathematics, Temple University
Venue:
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Year:
2011

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Abstract

We give the first data structure for the problem of maintaining a dynamic set of n elements drawn from a partially ordered universe described by a tree. We define the LINE-LEAF Tree, a linear-sized data structure that supports the operations: insert; delete; test membership; and predecessor. The performance of our data structure is within an O(log w)-factor of optimal. Here w ≤ n is the width of the partial-order--a natural obstacle in searching a partial order.