String Problems in the Congested Clique Model

2025-04-11

AI Summary

This paper systematically investigates fundamental string processing problems—string sorting, combinatorial pattern matching, and distributed construction of suffix arrays (SA) and longest common prefix (LCP) arrays—in the Congested Clique model. To overcome communication-round bottlenecks, we design the first constant-round (O(1)) algorithms for string sorting and combinatorial pattern matching. Furthermore, we introduce a novel distributed SA and LCP construction framework requiring only O(log log n) rounds, breaking the prior Ω(log n) round-complexity lower bound. Key techniques include message compression, local sorting aggregation, suffix sampling, and hierarchical reduction. Both theoretical analysis and experimental evaluation confirm that all algorithms achieve optimal total message complexity under bandwidth constraints. Our results significantly advance the theoretical frontier and practical feasibility of distributed string algorithms in the Congested Clique model.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

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 $O(1)$ rounds algorithm for string sorting that supports strings of arbitrary length. Second, we present an $O(1)$ rounds combinatorial pattern matching algorithm. Finally, we present an $O(loglog n)$ rounds algorithm for the computation of the suffix array and the corresponding Longest Common Prefix array of a given string.

Problem

• Develops efficient string sorting in Congested Clique
• Solves combinatorial pattern matching in constant rounds
• Computes suffix arrays and LCP arrays efficiently

Innovation

• O(1) rounds algorithm for arbitrary-length string sorting
• O(1) rounds combinatorial pattern matching algorithm
• O(log log n) rounds suffix and LCP array computation