Set Covering with our Eyes Closed

Given a universe U of n elements and a weighted collection S of m subsets of U, the universal set cover problem is to a-priori map each element u ∈ U to a set S(u) ∈ S containing u, so that X ⊆ U is covered by S(X) = ∪u∈X S(u). The aim is finding a mapping such that the cost of S(X) is as close as possible to the optimal set-cover cost for X. (Such problems are also called oblivious or a-priori optimization problems.) Universal algorithms are useful in distributed settings, where decisions are taken locally to minimize the communication overhead. Similarly, in critical applications one wants to pre-compute solutions for a family of scenarios, so as to react faster when the actual input shows up. Moreover, universal mappings can be translated into online algorithms. Unfortunately, for every universal mapping, if the set X is adversarially chosen, the cost of S(X) can be Ω( √ n) times larger than optimal (e.g., see Jia et al. [STOC’05]). However, in many applications, t...

• Type: Conference
• Year: 2008
• Where: FOCS
• Authors: Fabrizio Grandoni, Anupam Gupta, Stefano Leonardi, Pauli Miettinen, Piotr Sankowski, Mohit Singh
• Keywords: FOCS 2008, Greedy Algorithm, Theoretical Computer Science, Universal, Universal Mapping