2,581 research outputs found
Recursive Online Enumeration of All Minimal Unsatisfiable Subsets
In various areas of computer science, we deal with a set of constraints to be
satisfied. If the constraints cannot be satisfied simultaneously, it is
desirable to identify the core problems among them. Such cores are called
minimal unsatisfiable subsets (MUSes). The more MUSes are identified, the more
information about the conflicts among the constraints is obtained. However, a
full enumeration of all MUSes is in general intractable due to the large number
(even exponential) of possible conflicts. Moreover, to identify MUSes
algorithms must test sets of constraints for their simultaneous satisfiabilty.
The type of the test depends on the application domains. The complexity of
tests can be extremely high especially for domains like temporal logics, model
checking, or SMT. In this paper, we propose a recursive algorithm that
identifies MUSes in an online manner (i.e., one by one) and can be terminated
at any time. The key feature of our algorithm is that it minimizes the number
of satisfiability tests and thus speeds up the computation. The algorithm is
applicable to an arbitrary constraint domain and its effectiveness demonstrates
itself especially in domains with expensive satisfiability checks. We benchmark
our algorithm against state of the art algorithm on Boolean and SMT constraint
domains and demonstrate that our algorithm really requires less satisfiability
tests and consequently finds more MUSes in given time limits
Human-Centred Feasibility Restoration
Decision systems for solving real-world combinatorial problems must be able to report infeasibility in such a way that users can understand the reasons behind it, and understand how to modify the problem to restore feasibility. Current methods mainly focus on reporting one or more subsets of the problem constraints that cause infeasibility. Methods that also show users how to restore feasibility tend to be less flexible and/or problem-dependent. We describe a problem-independent approach to feasibility restoration that combines existing techniques from the literature in novel ways to yield meaningful, useful, practical and flexible user support. We evaluate the resulting framework on two real-world applications
Improving MCS Enumeration via Caching
Enumeration of minimal correction sets (MCSes) of conjunctive normal form formulas is a central and highly intractable problem in infeasibility analysis of constraint systems. Often complete enumeration of MCSes is impossible due to both high computational cost and worst-case exponential number of MCSes. In such cases partial enumeration is sought for, finding applications in various domains, including axiom pinpointing in description logics among others. In this work we propose caching as a means of further improving the practical efficiency of current MCS enumeration approaches, and show the potential of caching via an empirical evaluation.Peer reviewe
Core-guided minimal correction set and core enumeration
A set of constraints is unsatisfiable if there is no solution that satisfies these constraints. To analyse unsatisfiable problems, the user needs to understand where inconsistencies come from and how they can be repaired. Minimal unsatisfiable cores and correction sets are important subsets of constraints that enable such analysis. In this work, we propose a new algorithm for extracting minimal unsatisfiable cores and correction sets simultaneously. Building on top of the relaxation and strengthening framework, we introduce novel techniques for extracting these sets. Our new solver significantly outperforms several state of the art algorithms on common benchmarks when it comes to extracting correction sets and compares favorably on core extraction.Peer ReviewedPostprint (published version
Spatial Guilds in the Serengeti Food Web Revealed by a Bayesian Group Model
Food webs, networks of feeding relationships among organisms, provide
fundamental insights into mechanisms that determine ecosystem stability and
persistence. Despite long-standing interest in the compartmental structure of
food webs, past network analyses of food webs have been constrained by a
standard definition of compartments, or modules, that requires many links
within compartments and few links between them. Empirical analyses have been
further limited by low-resolution data for primary producers. In this paper, we
present a Bayesian computational method for identifying group structure in food
webs using a flexible definition of a group that can describe both functional
roles and standard compartments. The Serengeti ecosystem provides an
opportunity to examine structure in a newly compiled food web that includes
species-level resolution among plants, allowing us to address whether groups in
the food web correspond to tightly-connected compartments or functional groups,
and whether network structure reflects spatial or trophic organization, or a
combination of the two. We have compiled the major mammalian and plant
components of the Serengeti food web from published literature, and we infer
its group structure using our method. We find that network structure
corresponds to spatially distinct plant groups coupled at higher trophic levels
by groups of herbivores, which are in turn coupled by carnivore groups. Thus
the group structure of the Serengeti web represents a mixture of trophic guild
structure and spatial patterns, in contrast to the standard compartments
typically identified in ecological networks. From data consisting only of nodes
and links, the group structure that emerges supports recent ideas on spatial
coupling and energy channels in ecosystems that have been proposed as important
for persistence.Comment: 28 pages, 6 figures (+ 3 supporting), 2 tables (+ 4 supporting
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