arXiv subjects

Ciaran McCreesh

Publications and source records attributed to Ciaran McCreesh.

11 recordsLinked to original sources

arXiv2026

Introducing The Maximum Common Bigraph Problem

Bigraph reactive systems offer a powerful and flexible mathematical framework for modelling both spatial and non-spatial relationships between agents, with practical applications in domains such as smart technologies, networks, sensor systems, and biology. While bigraphs theoretically support the identification of bisimilar agents, by simulating and comparing their corresponding minimal contextual transition systems, no known algorithm exists for computing the maximum shared structure between two bigraphs, an essential prerequisite for determining the set of possible transitions for a given agent state. In this work, we provide a definition of the maximum common bigraph problem, and present an adaptation of the McSplit maximum common induced subgraph algorithm to compute the maximum common bigraph between two bigraph states. Our approach opens a path toward supporting bisimulation checking in bigraph-based tools, which have been leveraged in other modelling paradigms for simplification, optimisation, and verification of models.

cs.LO↗

arXiv2025

Faster Certified Symmetry Breaking Using Orders With Auxiliary Variables

Symmetry breaking is a crucial technique in modern combinatorial solving, but it is difficult to be sure it is implemented correctly. The most successful approach to deal with bugs is to make solvers certifying, so that they output not just a solution, but also a mathematical proof of correctness in a standard format, which can then be checked by a formally verified checker. This requires justifying symmetry reasoning within the proof, but developing efficient methods for this has remained a long-standing open challenge. A fully general approach was recently proposed by Bogaerts et al. (2023), but it relies on encoding lexicographic orders with big integers, which quickly becomes infeasible for large symmetries. In this work, we develop a method for instead encoding orders with auxiliary variables. We show that this leads to orders-of-magnitude speed-ups in both theory and practice by running experiments on proof logging and checking for SAT symmetry breaking using the state-of-the-art satsuma symmetry breaker and the VeriPB proof checking toolchain.

cs.LO↗

arXiv2023

Certified Symmetry and Dominance Breaking for Combinatorial Optimisation

Symmetry and dominance breaking can be crucial for solving hard combinatorial search and optimisation problems, but the correctness of these techniques sometimes relies on subtle arguments. For this reason, it is desirable to produce efficient, machine-verifiable certificates that solutions have been computed correctly. Building on the cutting planes proof system, we develop a certification method for optimisation problems in which symmetry and dominance breaking are easily expressible. Our experimental evaluation demonstrates that we can efficiently verify fully general symmetry breaking in Boolean satisfiability (SAT) solving, thus providing, for the first time, a unified method to certify a range of advanced SAT techniques that also includes XOR and cardinality reasoning. In addition, we apply our method to maximum clique solving and constraint programming as a proof of concept that the approach applies to a wider range of combinatorial problems.

cs.AI↗

arXiv2018

A Review of Literature on Parallel Constraint Solving

As multicore computing is now standard, it seems irresponsible for constraints researchers to ignore the implications of it. Researchers need to address a number of issues to exploit parallelism, such as: investigating which constraint algorithms are amenable to parallelisation; whether to use shared memory or distributed computation; whether to use static or dynamic decomposition; and how to best exploit portfolios and cooperating search. We review the literature, and see that we can sometimes do quite well, some of the time, on some instances, but we are far from a general solution. Yet there seems to be little overall guidance that can be given on how best to exploit multicore computers to speed up constraint solving. We hope at least that this survey will provide useful pointers to future researchers wishing to correct this situation. Under consideration in Theory and Practice of Logic Programming (TPLP).

cs.AI↗

arXiv2017

Replicable Parallel Branch and Bound Search

Combinatorial branch and bound searches are a common technique for solving global optimisation and decision problems. Their performance often depends on good search order heuristics, refined over decades of algorithms research. Parallel search necessarily deviates from the sequential search order, sometimes dramatically and unpredictably, e.g. by distributing work at random. This can disrupt effective search order heuristics and lead to unexpected and highly variable parallel performance. The variability makes it hard to reason about the parallel performance of combinatorial searches. This paper presents a generic parallel branch and bound skeleton, implemented in Haskell, with replicable parallel performance. The skeleton aims to preserve the search order heuristic by distributing work in an ordered fashion, closely following the sequential search order. We demonstrate the generality of the approach by applying the skeleton to 40 instances of three combinatorial problems: Maximum Clique, 0/1 Knapsack and Travelling Salesperson. The overheads of our Haskell skeleton are reasonable: giving slowdown factors of between 1.9 and 6.2 compared with a class-leading, dedicated, and highly optimised C++ Maximum Clique solver. We demonstrate scaling up to 200 cores of a Beowulf cluster, achieving speedups of 100x for several Maximum Clique instances. We demonstrate low variance of parallel performance across all instances of the three combinatorial problems and at all scales up to 200 cores, with median Relative Standard Deviation (RSD) below 2%. Parallel solvers that do not follow the sequential search order exhibit far higher variance, with median RSD exceeding 85% for Knapsack.

cs.DC↗

arXiv2014

A Parallel Branch and Bound Algorithm for the Maximum Labelled Clique Problem

The maximum labelled clique problem is a variant of the maximum clique problem where edges in the graph are given labels, and we are not allowed to use more than a certain number of distinct labels in a solution. We introduce a new branch-and-bound algorithm for the problem, and explain how it may be parallelised. We evaluate an implementation on a set of benchmark instances, and show that it is consistently faster than previously published results, sometimes by four or five orders of magnitude.

cs.DS↗

arXiv2014

Case Studies and Challenges in Reproducibility in the Computational Sciences

This paper investigates the reproducibility of computational science research and identifies key challenges facing the community today. It is the result of the First Summer School on Experimental Methodology in Computational Science Research (https://blogs.cs.st-andrews.ac.uk/emcsr2014/). First, we consider how to reproduce experiments that involve human subjects, and in particular how to deal with different ethics requirements at different institutions. Second, we look at whether parallel and distributed computational experiments are more or less reproducible than serial ones. Third, we consider reproducible computational experiments from fields outside computer science. Our final case study looks at whether reproducibility for one researcher is the same as for another, by having an author attempt to have others reproduce their own, reproducible, paper. This paper is open, executable and reproducible: the whole process of writing this paper is captured in the source control repository hosting both the source of the paper, supplementary codes and data; we are providing setup for several experiments on which we were working; finally, we try to describe what we have achieved during the week of the school in a way that others may reproduce (and hopefully improve) our experiments.

cs.CE↗

arXiv2014

The Shape of the Search Tree for the Maximum Clique Problem, and the Implications for Parallel Branch and Bound

Finding a maximum clique in a given graph is one of the fundamental NP-hard problems. We compare two multi-core thread-parallel adaptations of a state-of-the-art branch and bound algorithm for the maximum clique problem, and provide a novel explanation as to why they are successful. We show that load balance is sometimes a problem, but that the interaction of parallel search order and the most likely location of solutions within the search space is often the dominating consideration. We use this explanation to propose a new low-overhead, scalable work splitting mechanism. Our approach uses explicit early diversity to avoid strong commitment to the weakest heuristic advice, and late resplitting for balance. More generally, we argue that for branch and bound, parallel algorithm design should not be performed independently of the underlying sequential algorithm.

cs.DC↗

arXiv2014

Finding Maximum k-Cliques Faster using Lazy Global Domination

A clique in a graph is a set of vertices, each of which is adjacent to every other vertex in this set. A k-clique relaxes this requirement, requiring vertices to be within a distance k of each other, rather than directly adjacent. In theory, a maximum clique algorithm can easily be adapted to solve the maximum k-clique problem. We use a state of the art maximum clique algorithm to show that this is feasible in practice, and introduce a lazy global domination rule which sometimes vastly reduces the search space. We include experimental results for a range of real-world and benchmark graphs, and a detailed look at random graphs.

cs.DS↗

arXiv2013

Greedy Graph Colouring is a Misleading Heuristic

State of the art maximum clique algorithms use a greedy graph colouring as a bound. We show that greedy graph colouring can be misleading, which has implications for parallel branch and bound.

cs.DS↗

arXiv2012

Distributing an Exact Algorithm for Maximum Clique: maximising the costup

We take an existing implementation of an algorithm for the maximum clique problem and modify it so that we can distribute it over an ad-hoc cluster of machines. Our goal was to achieve a significant speedup in performance with minimal development effort, i.e. a maximum costup. We present a simple modification to a state-of-the-art exact algorithm for maximum clique that allows us to distribute it across many machines. An empirical study over large hard benchmarks shows that speedups of an order of magnitude are routine for 25 or more machines.

cs.DS↗