Recognition of three-dimensional objects, puzzle solving, electronic circuit analysis and truth-maintenance systems are examples of such problems, and these are normally solved by various versions of backtrack search. In this work we show how advice can be automatically generated to guide the order in which the search algorithm assigns values to the variables, so as to reduce the amount of backtracking. The advice is generated by consulting relaxed models of the subproblems created by each value-assignment candidate. The relaxed problems are chosen to yield backtrack-free solutions, and the information retrieved from these models induces a preference order among the choices pending in the original problem.

Problem solvers need more than just the facts and logic of a problem domain. To work effectively, they also aced meta-knowledge, that is, knowledge about how to use the facts. For example, hierarchical planning uses meta-knowledge to distinguish between the important considerations and the details of a problem. This knowledge is added to the facts and logic of a domain and used to focus the generation of inferences. It relieves a hierarchical planner from trying to deal with everything at once.

The cutting plane method is an augmentative constrained optimization procedure that is often used with continuous-domain optimization techniques such as linear and convex programs. We investigate the viability of a similar idea within message passing -- for integral solutions -- in the context of two combinatorial problems: 1) For Traveling Salesman Problem (TSP), we propose a factor-graph based on Held-Karp formulation, with an exponential number of constraint factors, each of which has an exponential but sparse tabular form. 2) For graph-partitioning (a.k.a. community mining) using modularity optimization, we introduce a binary variable model with a large number of constraints that enforce formation of cliques. In both cases we are able to derive surprisingly simple message updates that lead to competitive solutions on benchmark instances. In particular for TSP we are able to find near-optimal solutions in the time that empirically grows with $N^3$, demonstrating that augmentation is practical and efficient.

We consider the quantified constraint satisfaction problem (QCSP) which is to decide, given a structure and a first-order sentence (not assumed here to be in prenex form) built from conjunction and quantification, whether or not the sentence is true on the structure. We present a proof system for certifying the falsity of QCSP instances and develop its basic theory; for instance, we provide an algorithmic interpretation of its behavior. Our proof system places the established Q-resolution proof system in a broader context, and also allows us to derive QCSP tractability results.

Identifying important components or factors in large amounts of noisy data is a key problem in machine learning and data mining. Motivated by a pattern decomposition problem in materials discovery, aimed at discovering new materials for renewable energy, e.g. for fuel and solar cells, we introduce CombiFD, a framework for factor based pattern decomposition that allows the incorporation of a-priori knowledge as constraints, including complex combinatorial constraints. In addition, we propose a new pattern decomposition algorithm, called AMIQO, based on solving a sequence of (mixed-integer) quadratic programs. Our approach considerably outperforms the state of the art on the materials discovery problem, scaling to larger datasets and recovering more precise and physically meaningful decompositions. We also show the effectiveness of our approach for enforcing background knowledge on other application domains.

The Workflow Satisfiability Problem (WSP) is a problem of practical interest that arises whenever tasks need to be performed by authorized users, subject to constraints defined by business rules. We are required to decide whether there exists a plan - an assignment of tasks to authorized users - such that all constraints are satisfied. It is natural to see the WSP as a subclass of the Constraint Satisfaction Problem (CSP) in which the variables are tasks and the domain is the set of users. What makes the WSP distinctive is that the number of tasks is usually very small compared to the number of users, so it is appropriate to ask for which constraint languages the WSP is fixed-parameter tractable (FPT), parameterized by the number of tasks. This novel approach to the WSP, using techniques from CSP, has enabled us to design a generic algorithm which is FPT for several families of workflow constraints considered in the literature. Furthermore, we prove that the union of FPT languages remains FPT if they satisfy a simple compatibility condition. Lastly, we identify a new FPT constraint language, user-independent constraints, that includes many of the constraints of interest in business processing systems. We demonstrate that our generic algorithm has provably optimal running time O*(2^(klog k)), for this language, where k is the number of tasks.

The past decade has witnessed the rapid emergence of the We consider a central task in combinatorial materials discovery, field of human computation, along with numerous successful namely the problem of identifying the crystalline applications. Human computation is motivated by problems phases of inorganic compounds based on an analysis of for which automated algorithms cannot yet exceed high-intensity X-ray patterns. In our approach, we integrate human performance (Von Ahn 2005). Indeed, some tasks a state-of-the-art optimization framework based on are naturally and truly easy for humans, while they remain constraint reasoning with a human computation component.

Constructing a good conference schedule for a large multi-track conference needs to take into account the preferences and constraints of organizers, authors, and attendees. Creating a schedule which has fewer conflicts for authors and attendees, and thematically coherent sessions is a challenging task. Cobi introduced an alternative approach to conference scheduling by engaging the community to play an active role in the planning process. The current Cobi pipeline consists of committee-sourcing and author-sourcing to plan a conference schedule. We further explore the design space of community-sourcing by introducing attendee-sourcing -- a process that collects input from conference attendees and encodes them as preferences and constraints for creating sessions and schedule. For CHI 2014, a large multi-track conference in human-computer interaction with more than 3,000 attendees and 1,000 authors, we collected attendees’ preferences by making available all the accepted papers at the conference on a paper recommendation tool we built called Confer, for a period of 45 days before announcing the conference program (sessions and schedule). We compare the preferences marked on Confer with the preferences collected from Cobi’s author-sourcing approach. We show that attendee-sourcing can provide insights beyond what can be discovered by author-sourcing. For CHI 2014, the results show value in the method and attendees’ participation. It produces data that provides more alternatives in scheduling and complements data collected from other methods for creating coherent sessions and reducing conflicts.

This paper introduces a novel encoding of Model Based Diagnosis (MBD) to Boolean Satisfaction (SAT) focusing on minimal cardinality diagnosis. The encoding is based on a combination of sophisticated MBD preprocessing algorithms and the application of a SAT compiler which optimizes the encoding to provide more succinct CNF representations than obtained with previous works. Experimental evidence indicates that our approach is superior to all published algorithms for minimal cardinality MBD. In particular, we can determine, for the first time, minimal cardinality diagnoses for the entire standard ISCAS-85 and 74XXX benchmarks. Our results open the way to improve the state-of-the-art on a range of similar MBD problems.

RCC8 is a popular fragment of the region connection calculus, in which qualitative spatial relations between regions, such as adjacency, overlap and parthood, can be expressed. While RCC8 is essentially dimensionless, most current applications are confined to reasoning about two-dimensional or three-dimensional physical space. In this paper, however, we are mainly interested in conceptual spaces, which typically are high-dimensional Euclidean spaces in which the meaning of natural language concepts can be represented using convex regions. The aim of this paper is to analyze how the restriction to convex regions constrains the realizability of networks of RCC8 relations. First, we identify all ways in which the set of RCC8 base relations can be restricted to guarantee that consistent networks can be convexly realized in respectively 1D, 2D, 3D, and 4D. Most surprisingly, we find that if the relation 'partially overlaps' is disallowed, all consistent atomic RCC8 networks can be convexly realized in 4D. If instead refinements of the relation 'part of' are disallowed, all consistent atomic RCC8 relations can be convexly realized in 3D. We furthermore show, among others, that any consistent RCC8 network with 2n+1 variables can be realized using convex regions in the n-dimensional Euclidean space.