Less is More: Faster Maximum Clique Search by Work-Avoidance

2025-09-26

AI Summary

Maximum clique search—a classical NP-hard problem—suffers from prohibitively large search spaces and low computational efficiency. To address this, we propose an efficient algorithmic framework grounded in the “work-avoiding” paradigm. Our approach introduces four key innovations: (i) a lazy graph representation that defers structural construction until necessary; (ii) a prescreening mechanism enabling early pruning; (iii) optimized intersection computation with fast-exit semantics; and (iv) an adaptive algorithm selection strategy. Collectively, these techniques strengthen pruning power, drastically reducing both the number of visited search nodes and redundant computations. Evaluated on standard benchmarks, our method achieves up to 38.9× and 11× speedups over the state-of-the-art algorithms PMC and MC-BRB, respectively, significantly shortening runtime. The framework delivers a scalable, principled solution for maximum clique search on large-scale graphs.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Graph-based Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

The maximum clique (MC) problem is a challenging graph mining problem which, due to its NP-hard nature, can take a substantial amount of execution time. The MC problem is dominated by set intersection operations similar to Maximal Clique Enumeration, however it differs in requiring to find only a clique of maximum size. As such, key to the problem is to demonstrate efficiently that a particular part of the search space does not contain a maximum clique, allowing to skip over major parts of the search space. We present a number of techniques to optimize MC search in light of leaving major parts of the search space unvisited, including (i) an efficient, lazily constructed graph representation; (ii) filtering prior to initiating a detailed search; (iii) efficient early-exit intersection algorithms; (iv) exploiting algorithmic choice. These techniques result in a speedup of up to 38.9x compared to PMC, which is the most comparable algorithm, and a speedup up to 11x over MC-BRB.

Problem

• Optimizing maximum clique search via work-avoidance techniques
• Accelerating clique discovery by skipping unpromising search spaces
• Enhancing efficiency through lazy graphs and early-exit intersections

Innovation

• Efficient lazy graph representation construction
• Filtering before detailed search initiation
• Early-exit intersection algorithms optimization