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Emma Rollon

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8 papers

2 author rows

AAAI Conference 2024 Conference Paper

Theoretical and Empirical Analysis of Cost-Function Merging for Implicit Hitting Set WCSP Solving

Javier Larrosa
Conrado Martínez
Emma Rollon

The Implicit Hitting Set (HS) approach has shown very effective for MaxSAT solving. However, only preliminary promising results have been obtained for the very similar Weighted CSP framework. In this paper we contribute towards both a better theoretical understanding of the HS approach and a more effective HS-based solvers for WCSP. First, we bound the minimum number of iterations of HS thanks to what we call distinguished cores. Then, we show a source of inefficiency by introducing two simple problems where HS is unfeasible. Next, we propose two reformulation methods that merge cost-functions to overcome the problem. We provide a theoretical analysis that quantifies the magnitude of the improvement of each method with respect to the number of iterations of the algorithm. In particular, we show that the reformulations can bring an exponential number of iterations down to a constant number in our working examples. Finally, we complement our theoretical analysis with two sets of experiments. First, we show that our results are aligned with real executions. Second, and most importantly, we conduct experiments on typical benchmark problems and show that cost-function merging may be heuristically applied and it may accelerate HS algorithms by several orders of magnitude. In some cases, it even outperforms state-of-the-art solvers.

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AAAI Conference 2020 Conference Paper

Augmenting the Power of (Partial) MaxSat Resolution with Extension

Javier Larrosa
Emma Rollon

The refutation power of SAT and MaxSAT resolution is challenged by problems like the soft and hard Pigeon Hole Problem PHP for which short refutations do not exist. In this paper we augment the MaxSAT resolution proof system with an extension rule. The new proof system MaxResE is sound and complete, and more powerful than plain MaxSAT resolution, since it can refute the soft and hard PHP in polynomial time. We show that MaxResE refutations actually subtract lower bounds from the objective function encoded by the formulas. The resulting formula is the residual after the lower bound extraction. We experimentally show that the residual of the soft PHP (once its necessary cost of 1 has been efﬁciently subtracted with MaxResE) is a concise, easy to solve, satisﬁable problem.

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SAT Conference 2020 Conference Paper

Towards a Better Understanding of (Partial Weighted) MaxSAT Proof Systems

Javier Larrosa
Emma Rollon

Abstract MaxSAT is a very popular language for discrete optimization with many domains of application. While there has been a lot of progress in MaxSAT solvers during the last decade, the theoretical analysis of MaxSAT inference has not followed the pace. Aiming at compensating that lack of balance, in this paper we do a proof complexity approach to MaxSAT resolution-based proof systems. First, we give some basic definitions on completeness and show that refutational completeness makes compleness redundant, as it happens in SAT. Then we take three inference rules such that adding them sequentially allows us to navigate from the weakest to the strongest resolution-based MaxSAT system available (i. e. , from standalone MaxSAT resolution to the recently proposed ResE), each rule making the system stronger. Finally, we show that the strongest system captures the recently proposed concept of Circular Proof while being conceptually simpler, since weights, which are intrinsic in MaxSAT, naturally guarantee the flow condition required for the SAT case.

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IJCAI Conference 2016 Conference Paper

Limited Discrepancy AND/OR Search and Its Application to Optimization Tasks in Graphical Models

Javier Larrosa
Emma Rollon
Rina Dechter

Many combinatorial problems are solved with a Depth-First search (DFS) guided by a heuristic and it is well-known that this method is very fragile with respect to heuristic mistakes. One standard way to make DFS more robust is to search by increasing number of discrepancies. This approach has been found useful in several domains where the search structure is a height-bounded OR tree. In this paper we investigate the generalization of discrepancy-based search to AND/OR search trees and propose an extension of the Limited Discrepancy Search (LDS) algorithm. We demonstrate the relevance of our proposal in the context of Graphical Models. In these problems, which can be solved with either a standard OR search tree or an AND/OR tree, we show the superiority of our approach. For a fixed number of discrepancies, the search space visited by the AND/OR algorithm strictly contains the search space visited by standard LDS, and many more nodes can be visited due to the multiplicative effect of the AND/OR decomposition. Besides, if the AND/OR tree achieves a significant size reduction with respect to the standard OR tree, the cost of each iteration of the AND/OR algorithm is asymptotically lower than in standard LDS. We report experiments on the minsum problem on different domains and show that the AND/OR version of LDS usually obtains better solutions given the same CPU time.

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IJCAI Conference 2013 Conference Paper

Semiring-Based Mini-Bucket Partitioning Schemes

Emma Rollon
Javier Larrosa
Rina Dechter

Graphical models are one of the most prominent frameworks to model complex systems and efficiently query them. Their underlying algebraic properties are captured by a valuation structure that, most usually, is a semiring. Depending on the semiring of choice, we can capture probabilistic models, constraint networks, cost networks, etc. In this paper we address the partitioning problem which occurs in many approximation techniques such as mini-bucket elimination and joingraph propagation algorithms. Roghly speaking, subject to complexity bounds, the algorithm needs to find a partition of a set of factors such that best approximates the whole set. While this problem has been addressed in the past in a particular case, we present here a general description. Furthermore, we also propose a general partitioning scheme. Our proposal is general in the sense that it is presented in terms of a generic semiring with the only additional requirements of a division operation and a refinement of its order. The proposed algorithm instantiates to the particular task of computing the probability of evidence, but also applies directly to other important reasoning tasks. We demonstrate its good empirical behaviour on the problem of computing the most probable explanation.

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AAAI Conference 2010 Conference Paper

New Mini-Bucket Partitioning Heuristics for Bounding the Probability of Evidence

Emma Rollon
Rina Dechter

Mini-Bucket Elimination (MBE) is a well-known approximation algorithm deriving lower and upper bounds on quantities of interest over graphical models. It relies on a procedure that partitions a set of functions, called bucket, into smaller subsets, called mini-buckets. The method has been used with a single partitioning heuristic throughout, so the impact of the partitioning algorithm on the quality of the generated bound has never been investigated. This paper addresses this issue by presenting a framework within which partitioning strategies can be described, analyzed and compared. We derive a new class of partitioning heuristics from first-principles geared for likelihood queries, demonstrate their impact on a number of benchmarks for probabilistic reasoning and show that the results are competitive (often superior) to state-ofthe-art bounding schemes.

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AAAI Conference 2007 Conference Paper

Multi-Objective Russian Doll Search

Emma Rollon

Russian Doll Search (RDS) is a well-known algorithm for combinatorial optimization. In this paper we extend it from mono-objective to multi-objective optimization. We demonstrate its practical applicability in the challenging multipleorbit SPOT5 instances. Besides being much more efﬁcient than any other alternatives, multi-objective RDS can solve an instance which could not have been solved previously.

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ECAI Conference 2006 Conference Paper

Multi-Objective Propagation in Constraint Programming

Emma Rollon
Javier Larrosa

Bounding constraints are used to bound the tolerance of solutions under certain undesirable features. Standard solvers propagate them one by one. Often times, it is easy to satisfy them independently, but difficult to satisfy them simultaneously. Therefore, the standard propagation methods fail. In this paper we propose a novel approach inspired in multi-objective optimization. We compute a multi-objective lower bound set that, if large enough, can be used to detect the inconsistency of the problem. Our experiments on two domains inspired in real-world problems show that propagation of additive bounding constraints using our approach is clearly superior than previous approaches.

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