DMC: A Distributed Model Counter

Abstract

We present and evaluate DMC, a distributed model counter for propositional CNF formulae based on the state-of-the-art sequential model counter D4. DMC can take advantage of a (possibly large) number of sequential model counters running on (possibly heterogeneous) computing units spread over a network of computers. For ensuring an efficient workload distribution, the model counting task is shared between the model counters following a policy close to work stealing. The number and the sizes of the messages which are exchanged by the jobs are kept small. The results obtained show DMC as a much more efficient counter than D4, the distribution of the computation yielding large improvements for some benchmarks. DMC appears also as a serious challenger to the parallel model counter CountAntom and to the distributed model counter dCountAntom.

Advanced tools and methods for treewidth-based problem solving

“…We also included multi-core solvers dpdb [Fichte et al, 2021b], gpusat2 [Fichte et al, 2019b], as well as countAntom [Burchard et al, 2015]. Note that we excluded distributed solvers such as dCountAntom [Burchard et al, 2016] and DMC [Lagniez et al, 2018] much on the instances. Further, we observed that the employed simple cache as used in Listing 3.1, provides only a marginal improvement.…”

“…• Counting the number of models of a Boolean formula (#Sat) [Gomes et al, 2009], which recently fostered different applications and solving techniques [Lagniez and Marquis, 2014;Chakraborty et al, 2016;Dueñas-Osorio et al, 2017;Lagniez et al, 2018;Fichte et al, 2018c;Sharma et al, 2019].…”

Solving Projected Model Counting by Utilizing Treewidth and its Limits

“…For a more ample description of the used techniques, we refer to the model counting competition report [19]. Note that we excluded distributed solvers such as dCountAntom [88] and DMC [89] from our experimental setup. Both solvers require a cluster with access to the OpenMPI framework [90] and fast physical interconnections.…”

Knowledge compilation languages as proof systems

“…It has been observed by Huang and Darwiche [12] that these tools were implicitly constructing a dec-DNNF equivalent to the input formula. Tools such as c2d [19], D4 [15] or DMC [16] already exploit this connection and have the option to directly output an equivalent dec-DNNF. These solvers explore the set of satisfying assignments by branching on variables of the formula which correspond to a decision node and, when two variable independent components of the formula are detected, compute the number of satisfying assignments of both components and take the product, which corresponds to a decomposable ∧-gate.…”