Tarik Hadzic

Approximate Compilation of Constraints into Multivalued Decision Diagrams

We present an incremental refinement algorithm for approximate compilation of constraint satisfaction models into multivalued decision diagrams (MDDs). The algorithm uses a vertex splitting operation that relies on the detection of equivalent paths in the MDD. Although the algorithm is quite general, it can be adapted to exploit constraint structure by specializing the equivalence tests for partial assignments to particular constraints. We show how to modify the algorithm in a principled way to obtain an approximate MDD when the exact MDD is too large for practical purposes. This is done by replacing the equivalence test with a constraint-specific measure of distance. We demonstrate the value of the approach for approximate and exact MDD compilation and evaluate its benefits in one of the main MDD application domains, interactive configuration.

Real-Time Pedestrian Evacuation Planning during Emergency

We develop a set of solution techniques for real-time evacuation guidance of pedestrians during emergency, focusing on evacuation from buildings during a fire. We model the problem as an extension of a dynamic network flow by allowing for nodes and edges to expire over time. This captures evacuation situations where the spreading hazard renders parts of the network unavailable. We formally state the problem, analyze its complexity, develop a set of heuristic approaches and compare their performance against a number of most relevant alternative approaches. We experimentally demonstrate that our heuristics outperform the alternatives and are suitable for real-time use even for large networks.

Interactive cost configuration over decision diagrams

In many AI domains such as product configuration, a user should interactively specify a solution that must satisfy a set of constraints. In such scenarios, offline compilation of feasible solutions into a tractable representation is an important approach to delivering efficient backtrack-free user interaction online. In particular, binary decision diagrams (BDDs) have been successfully used as a compilation target for product and service configuration. In this paper we discuss how to extend BDD-based configuration to scenarios involving cost functions which express user preferences. We first show that an efficient, robust and easy to implement extension is possible if the cost function is additive, and feasible solutions are represented using multi-valued decision diagrams (MDDs). We also discuss the effect on MDD size if the cost function is non-additive or if it is encoded explicitly into MDD. We then discuss interactive configuration in the presence of multiple cost functions. We prove that even in its simplest form, multiple-cost configuration is NP-hard in the input MDD. However, for solving two-cost configuration we develop a pseudo-polynomial scheme and a fully polynomial approximation scheme. The applicability of our approach is demonstrated through experiments over real-world configuration models and product-catalogue datasets. Response times are generally within a fraction of a second even for very large instances.

Propagating separable equalities in an MDD store

We present a propagator that achieves MDD consistency for a separable equality over an MDD (multivalued decision diagram) store in pseudo-polynomial time.We integrate the propagator into a constraint solver based on an MDD store introduced in [1]. Our experiments show that the new propagator provides substantial computational advantage over propagation of two inequality constraints, and that the advantage increases when the maximum width of the MDD store increases.

A resource cost aware cumulative

We motivate and introduce an extension of the well-known cumulative constraint which deals with time and volume dependent cost of resources. Our research is primarily interested in scheduling problems under time and volume variable electricity costs, but the constraint equally applies to manpower scheduling when hourly rates differ over time and/or extra personnel incur higher hourly rates.We present a number of possible lower bounds on the cost, including a min-cost flow, different LP and MIP models, as well as greedy algorithms, and provide a theoretical and experimental comparison of the different methods.

Explanations and Relaxations for Policy Conflicts in Physical Access Control

Physical access control policies define sets of rulesthat govern peoples access to physical resources such asrooms and buildings. While simple decision-precedence can be used to reconcile different rules that result in conflicting access decisions, the presence of rule conflicts and other rule anomalies can make it difficult for a policy-administrator to comprehend and effectively manage complex policies. In this paper we are concerned with discovering conflicts and computing relaxations of access policies in order to eliminate conflicting rule instances. We propose several SAT based encodings in which these rule conflicts and anomalies areexpressed as explanation style problems. Relaxation techniques are in turn used to eliminate these anomalies by recommending what rules have to be revoked or what permissions have to beremoved from which rules. Moreover, we discuss a relaxation strategy that preserves most of the access constraints of theoriginal policy. Finally we provide a preliminary performancestudy of our techniques. Our approach is applicable to access control policies in general.

Enhanced Inference for the Market Split Problem

Inference in constraint programming is usually based on the deductions generated by individual constraints which are then communicated to other constraints through domain filtering. Frequently we find that this is a too coarse-grained form of communication since constraints could exchange more powerful forms of deductions that could help reduce the search effort. In this paper we propose a particular technique for enhancing inference in constraint programming, by generating deductions that involve tighter interleaving of constraints. We apply our method to the Market Split Problem and obtain massive speed-ups which brings a new order of Market Split Problems into the realm of solvability by means of constraint programming.

Layer Compression in Decision Diagrams

A number of compact representation forms that are investigated in the knowledge compilation community are utilized in interactive product configuration and other forms of decision support. Multi-valued decision diagrams (MDDs) are particularly well suited for interactive configuration. However, for large variable domains MDDs can be unnecessarily large if many values are repeating on different edges. In this paper we suggest exploiting the repetitive occurrences of values through the introduction of pseudo-nodes. The technique can be easily applied over MDDs as well as their more succinct counterpart, interval decision diagrams (IDDs). The compactness of the resulting representations, layer-compressed MDDs (lcMDDs) and layer-compressed IDDs (lcIDDs), is demonstrated empirically on artificial and real-world instances.

Constraint Programming Approach for Spatial Packaging Problem

The Spatial Packaging Problem (SPP) aims to solve a mixture of the 3D Packing Problem (3DPP) and the 3D Pipe-Routing Problem. The main feature that distinguishes the SPP from the traditional 3DPP is the interconnections that exist between its components. The SPP is more challenging because the shape and dimensions of the interconnections are unknown, and must be determined as part of the solution. In this paper, we propose a relaxation, a constraint programming model and a search heuristic to solve the SPP. We relax the SPP by using taxicab geometry and model it as a constraint satisfaction problem, then solve it by using a search heuristic based on interconnection volumes. The proposed approach has been evaluated on a challenging benchmark that reflects a range of aerospace and commercial applications varying in number of components and interconnections. The preliminary results show the effectiveness and efficiency of the proposed approach.

Uncovering functional dependencies in MDD-compiled product catalogues

A functional dependency is a logical relationship amongst the attributes that define a table of data. Specifically, a functional dependency holds when the values of a subset of the attributes in a dataset determine the values of one or more other attributes. Uncovering such dependencies is utilized in many domains, such as database design. We demonstrate that it can also be utilized in a recommendation context when datasets represent product catalogues. State-of-the-art approaches to discovering functional dependencies require a tabular representation of the data. However, product catalogues can sometimes be defined implicitly, for example, as a set of solutions to a combinatorial problem. Such combinatorial catalogues can have a very large number of products, thus making standard approaches to uncovering functional dependencies inapplicable. In this paper we present the first approach to computing functional dependencies over compiled knowledge representations which can often be small even for huge catalogues. In particular, we develop efficient algorithms that operate over decision diagrams, which allow us to handle catalogues that are out of reach for current approaches. We apply our algorithms to tabular and combinatorial benchmarks and detect a number of properties that could be considered as anomalies in product catalogues.