Constant-Time Local Computation Algorithms

Yishay Mansour, Boaz Patt-Shamir, Shai Vardi

Abstract: Local computation algorithms (LCAs) produce small parts of a single solution to a given search problem using time and space sublinear in the size of the input. In this work we present LCAs whose time complexity (and usually also space complexity) is independent of the input size. Specifically, we give (1) a $$(1-\epsilon )$$ -approximation LCA to the maximal weighted base of a graphic matroid (i.e., maximal acyclic edge set), (2) LCAs for approximating multicut and integer multicommodity flow on trees, and (3) a local reduction of weighted matching to any unweighted matching LCA, such that the running time of the weighted matching LCA is also independent of the edge weight function.