String problems in the congested clique model

Abstract

In this paper we present algorithms for several string problems in the Congested Clique model. In the Congested Clique model, n nodes (computers) are used to solve some problem. The input to the problem is distributed among the nodes, and the communication between the nodes is conducted in rounds. In each round, every node is allowed to send an $$O(\log n)$$ -bit message to every other node in the network. We consider three fundamental string problems in the Congested Clique model. First, we present an O(1)-round algorithm for string sorting. Second, we present an O(1)-round combinatorial pattern matching algorithm. Finally, we present an $$O(\log \log n)$$ -round algorithm for the computation of the Suffix Array and the corresponding Longest Common Prefix array of a given string. To obtain these algorithms, we develop a sorting procedure for large keys of polynomial size, extending the prior sorting algorithm of Lenzen [PODC’13], which handles only $$O(\log n)$$ -bit keys. This new procedure may be of independent interest.