Summary: On Local Search for Weighted k­Set Packing \Lambda
Esther M. Arkin y Refael Hassin z
August 12, 1997
Abstract
Given a collection of sets of cardinality at most k, with weights for each set, the
maximum weighted packing problem is that of finding a collection of disjoint sets of
maximum total weight. We study the worst case behavior of the t­local search heuristic
for this problem proving a tight bound of k \Gamma 1 + 1
t
. As a consequence, for any given
r ! 1
k\Gamma1
we can compute in polynomial time a solution whose weight is at least r times
the optimal.
1 Introduction
Maximum packing problems are among the most often studied in combinatorial optimiza­
tion: Given a collection X 1 ; : : : ; X q of k­sets, find a largest collection of pairwise disjoint sets
among them. One of the most fundamental packing problems is that of finding a maximum
matching in a graph; this problem is polynomially solvable. However, many other pack­
ing problems are NP­hard, including maximum 3­dimensional matching, maximum triangle

Source: Arkin, Estie - Department of Applied Mathematics and Statistics, SUNY at Stony Brook

Collections: Mathematics