We investigate the problem of cost-optimal planning in ASP. Current ASP planners can be trivially extended to a cost-optimal one by adding weak constraints, but only for a given makespan (number of steps). It is desirable to have a planner that guarantees global optimality. In this paper, we present two approaches to addressing this problem. First, we show how to engineer a cost-optimal planner composed of two ASP programs running in parallel. Using lessons learned from this, we then develop an entirely new approach to cost-optimal planning, stepless planning, which is completely free of makespan. Experiments to compare the two approaches with the only known cost-optimal planner in SAT reveal good potentials for stepless planning in ASP. The paper is under consideration for acceptance in TPLP.
Our 2-threaded solver algorithm is inspired by the approach of @cite_19 . The better performance of our planner, besides solver technologies, seems partly due to the grounding size and search space pruning under stable model semantics as commented in Section , and partly due to less clustered encoding in ASP than in SAT, plus the smart encoding of mutex constraints. But note that their approach works only if we assume the problem is solvable (which he does) and all actions have positive (nonzero) costs (which he also does).
@cite_19
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This work presents a novel strategy for improving SAT solver performance by using concurrency. Rather than aiming to parallelize search, we use concurrency to aid a conventional CDCL search procedure. More concretely, our work extends a conventional CDCL SAT solver with a second computation thread, which is solely used to strengthen the clauses learned by the solver. This provides a simple and natural way to exploit the availability of multi-core hardware. We have employed our technique to extend two well established solvers, MiniSAT and Glucose. Despite its conceptual simplicity the technique yields a significant improvement of those solvers' performances, in particular for unsatisfiable benchmarks. For such benchmarks an extensive empirical evaluation revealed a remarkably consistent reduction of the wall clock time required to determine unsatisfiability, as well as an ability to solve more benchmarks in the same CPU time. The proposed technique can be applied in combination with existing parallel SAT solving techniques, including both portfolio and search space splitting approaches. The approach presented here can thus be seen as orthogonal to those existing techniques. Motivated by the recent developments of nonconvex penalties in sparsity modeling, we propose a nonconvex optimization model for handing the low-rank matrix recovery problem. Different from the famous robust principal component analysis (RPCA), we suggest recovering low-rank and sparse matrices via a nonconvex loss function and a nonconvex penalty. The advantage of the nonconvex approach lies in its stronger robustness. To solve the model, we devise a majorization-minimization augmented Lagrange multiplier (MM-ALM) algorithm which finds the local optimal solutions of the proposed nonconvex model. We also provide an efficient strategy to speedup MM-ALM, which makes the running time comparable with the state-of-the-art algorithm of solving RPCA. Finally, empirical results demonstrate the superiority of our nonconvex approach over RPCA in terms of matrix recovery accuracy. We present a new efficient algorithm for the search version of the approximate Closest Vector Problem with Preprocessing (CVPP). Our algorithm achieves an approximation factor of O(n sqrt log n ), improving on the previous best of O(n^ 1.5 ) due to Lag arias, Lenstra, and Schnorr hkzbabai . We also show, somewhat surprisingly, that only O(n) vectors of preprocessing advice are sufficient to solve the problem (with the slightly worse approximation factor of O(n)). We remark that this still leaves a large gap with respect to the decisional version of CVPP, where the best known approximation factor is O(sqrt n log n ) due to Aharonov and Regev AharonovR04 . To achieve these results, we show a reduction to the same problem restricted to target points that are close to the lattice and a more efficient reduction to a harder problem, Bounded Distance Decoding with preprocessing (BDDP). Combining either reduction with the previous best-known algorithm for BDDP by Liu, Lyubashevsky, and Micciancio LiuLM06 gives our main result. In the setting of CVP without preprocessing, we also give a reduction from (1+eps)gamma approximate CVP to gamma approximate CVP where the target is at distance at most 1+1 eps times the minimum distance (the length of the shortest non-zero vector) which relies on the lattice sparsification techniques of Dadush and Kun DadushK13 . As our final and most technical contribution, we present a substantially more efficient variant of the LLM algorithm (both in terms of run-time and amount of preprocessing advice), and via an improved analysis, show that it can decode up to a distance proportional to the reciprocal of the smoothing parameter of the dual lattice MR04 . We show that this is never smaller than the LLM decoding radius, and that it can be up to an wide tilde Omega (sqrt n ) factor larger. Several message passing-based parallel solvers have been developed for general (non-symmetric) sparse LU factorization with partial pivoting. Existing solvers were mostly deployed and evaluated on parallel computing platforms with high message passing performance (e.g., 1-10 µs in message latency and 100-1000Mbytes s in message throughput) while little attention has been paid on slower platforms. This paper investigates techniques that are specifically beneficial for LU factorizafion on platforms with slow message passing. In the context of the S+ distributed memory solver, we find that significant reduction in the application message passing overhead can be attained at the cost of extra computation and slightly weakened numerical stability. In particular, we propose batch pivoting to make pivot selections in groups through speculative factorization, and thus substantially decrease the inter-processor synchronization granularity. We experimented on three different message passing platforms with different communication speeds. While the proposed techniques provide no performance benefit and even slightly weaken numerical stability on an IBM Regatta multiprocessor with fast message passing, they improve the performance of our test matrices by 15-460 on an Ethernet-connected 16-node PC cluster. Given the different tradeoffs of communication-reduction techniques on different message passing platforms, we also propose a sampling-based runtime application adaptation approach that automatically determines whether these techniques should be employed for a given platform and input matrix.