On Multi-dimensional Packing Problems

نویسنده

Minos N. Garofalakis

چکیده

line and oo-line approximation algorithms for vector covering problems. analysis of algorithms for dual bin packing problems. packing can be solved within 1 + in linear time.gorithms for the m-dimensional 0-1 knapsack problem: worst-case and probabilistic analyses.schatz. Resource scheduling in enhanced pay-per-view continuous media databases. An eecient approximation scheme for the one-dimensional bin-packing problem. probabilistic analysis of multi-dimensional bin packing problems. A polynomial time approximation scheme for maximizing the minimum completion time. 9 a reduction from the optimization version of bounded 3-Dimensional matching (3DM) problem 12]. We deene the problem formally below. Given a set T X Y Z. A matching in T is a subset M T such that no elements in M agree in any coordinate. The goal is to nd a matching in T of largest cardinality. A 3-bounded instance is one in which the number of occurrences of any element of X Y Z in T is at most 3. Kann 22] showed that the above problem is Max-SNP Complete (hence also APX-Complete). Our reduction builds on the ideas used in the NP-Completeness reduction that reduces the 3DM problem to the 4-Partition problem 12]. Let q = maxfjXj; jY j; jZjg, u = jX Y Zj and t = jTj. We create a total of (u + t) 2-dimensional vectors. We have one vector each for the elements of T and one for each of the elements of X Y Z.

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