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The fastest known exact algorithms for scorebased structure discovery inBayesian networks on n nodes run in time and space 2nnO(1). The usage of thesealgorithms is limited to networks on at most around 25 nodes mainly due to thespace requirement. Here, we study space-time tradeoffs for finding an optimalnetwork structure. When little space is available, we apply the Gurevich-Shelahrecurrence-originally proposed for the Hamiltonian path problem-and obtain time22n-snO(1) in space 2snO(1) for any s = n/2, n/4, n/8, . . .; we assume theindegree of each node is bounded by a constant. For the more practical settingwith moderate amounts of space, we present a novel scheme. It yields runningtime 2n(3/2)pnO(1) in space 2n(3/4)pnO(1) for any p = 0, 1, . . ., n/2; thesebounds hold as long as the indegrees are at most 0.238n. Furthermore, thelatter scheme allows easy and efficient parallelization beyond previousalgorithms. We also explore empirically the potential of the presentedtechniques.

Exact Structure Discovery in Bayesian Networks with Less Space