International Competition on Graph Counting Algorithms 2023

TL;DR

The paper details the 2023 International Competition on Graph Counting Algorithms, highlighting the challenge of counting constrained subgraphs in graphs resembling infrastructure networks, and evaluating diverse solver approaches.

Contribution

It introduces a competitive benchmarking framework for graph counting algorithms, compares multiple solver strategies, and provides insights into their strengths and limitations.

Findings

TLDC solver achieved the highest accuracy on benchmark instances.

Different approaches like backtracking, dynamic programming, and #SAT have unique advantages.

The competition highlights the complexity and diversity of graph counting problems.

Abstract

This paper reports on the details of the International Competition on Graph Counting Algorithms (ICGCA) held in 2023. The graph counting problem is to count the subgraphs satisfying specified constraints on a given graph. The problem belongs to #P-complete, a computationally tough class. Since many essential systems in modern society, e.g., infrastructure networks, are often represented as graphs, graph counting algorithms are a key technology to efficiently scan all the subgraphs representing the feasible states of the system. In the ICGCA, contestants were asked to count the paths on a graph under a length constraint. The benchmark set included 150 challenging instances, emphasizing graphs resembling infrastructure networks. Eleven solvers were submitted and ranked by the number of benchmarks correctly solved within a time limit. The winning solver, TLDC, was designed based on three fundamental approaches: backtracking search, dynamic programming, and model counting or #SAT (a counting version of Boolean satisfiability). Detailed analyses show that each approach has its own strengths, and one approach is unlikely to dominate the others. The codes and papers of the participating solvers are available: https://afsa.jp/icgca/.