Multiple-Winners Randomized Tournaments with Consensus for Optimization Problems in Generic Metric Spaces

Abstract. Extensions of the randomized tournaments techniques introduced in [6, 7] to approximate solutions of 1-median and diameter computation of finite subsets of general metric spaces are proposed. In the linear algorithms proposed in [6] (resp. [7]) randomized tournaments are played among the elements of an input subset S of a metric space. At each turn the residual set of winners is randomly partitioned in nonempty disjoint subsets of fixed size. The 1-median (resp. diameter) of each subset goes to the next turn whereas the residual elements are discarded. The algorithm proceeds recursively until a residual set of cardinality less than a given threshold is generated. The 1-median (resp. diameter) of such residual set is the approximate 1-median (resp. diameter) of the input set S. The O(n log n) extensions proposed in this paper replace local single-winner tournaments by multiple-winners ones. Moreover consensus is introduced as multiple runs of the same tournament. Experiments...

• Type: Conference
• Year: 2005
• Where: WEA
• Authors: Domenico Cantone, Alfredo Ferro, Rosalba Giugno, Giuseppe Lo Presti, Alfredo Pulvirenti
• Keywords: Algorithms, Metric Space, Nonempty Disjoint Subsets, Residual Set, WEA 2005