On the complexity of the view-selection problem

Abstract

A commonly used and powerful technique for improving query response time over very large databases is to precompute (‘Lmaterialize”) frequently’ asked queries (“views”). The problem is to select an appropriate set of views, given a limited amount of resources. Harinarayan, Rajaraman and Ullman formalized this technique by proposing a framework in which queries are modeled by a weighted partial order, and selecting a set of views whose materialization minimizes the average query response time is equivalent to selecting a subset of nodes of the partial order that minimizes a suitably defined cost function. Because this problem is NPHard, the focus is on approximability and heuristics. Harinarayan, Rajaraman and Ullman proposed a greedy heuristic together with a “benefit” criterion to measure its performance; this heuristic and performance measure are used in several subsequent papers which generalize their work. We prove the following lower bounds: (a) The greedy heuristic of Harinarayan, Rajaraman and Ullman has query response time at least n/12 times optimal for infinitely many n. (Compare this to the fact that no algorithm, regardless of how naive it is, ever has query response time exceeding n times optimal.) (b) If PfNP, then for every e > 0, every polynomialtime approximation algorithm for the view-selection problem will output solutions with query response time at least n’-’ times optimal, for infinitely many n, even for partial orders with bounded degrees and *College of Computing, Georgia Institute of Technology, howardQcc.gatech.edu. Research supported in part by NSF grant CCR-9732746. +CoIlege of Computing and School of Industrial and Systems Engineering, Georgia Institute of Technology, mihailQcc.gatech.edu. Work done in part while the author was at Bellcore. Permission to make digital or hard copies of all OT part of this work fbl personal or classroom USC is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this nhx and the full citation on the tirst page. TO COj>y otllerwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission andior a fee. PODS ‘99 Philadelphia PA Copyright ACM 1999 l-58113-062-7/99/05...$5.00 bounded depth. (c) A similar result applies even if we generously allow the algorithm to materialize ak views, LY a constant, and compare its performance to the optimal achievable when k views are chosen. Our results prove (if P#NP) that the viewselection problem is essentially inapproximable for general partial orders (the “benefit” performance measure of Harinarayan, Rajaraman and Ullman provides no competitiveness guarantee against the optimal solution). Hence studies of the Harinarayan, Rajaraman and Ullman framework and its generalizations should focus on special cases of practical significance, such as hypercubes, and on experimental comparison of heuristics.