Stéphane Zampelli

Solving subgraph isomorphism problems with constraint programming

The subgraph isomorphism problem consists in deciding if there exists a copy of a pattern graph in a target graph. We introduce in this paper a global constraint and an associated filtering algorithm to solve this problem within the context of constraint programming. The main idea of the filtering algorithm is to label every node with respect to its relationships with other nodes of the graph, and to define a partial order on these labels in order to express compatibility of labels for subgraph isomorphism. This partial order over labels is used to filter domains. Labelings can also be strengthened by adding information from the labels of neighbors. Such a strengthening can be applied iteratively until a fixpoint is reached. Practical experiments illustrate that our new filtering approach is more effective on difficult instances of scale free graphs than state-of-the-art algorithms and other constraint programming approaches.

Approximate constrained subgraph matching

Our goal is to build a declarative framework for approximate graph matching where various constraints can be stated upon the pattern graph, enabling approximate constrained subgraph matching, extending models and constraints proposed by Rudolf [1] and Valiente et al. [2]. In the present work, we propose a CSP approach for approximate subgraph matching where the potential approximation is declaratively stated in the pattern graph as mandatory/optional nodes/edges. Forbidden edges, that is edges that may not be included in the matching, can be declared on the pattern graph. We also want to declare properties between pairs of nodes in the pattern graph, such as distance properties, that can be either stated by the user, or automatically inferred by the system. In the former case, such properties can define new approximate patterns. In the latter case, these redundant constraints enhance the pruning.

Filtering for subgraph isomorphism

A subgraph isomorphism problem consists in deciding if there exists a copy of a pattern graph in a target graph. We introduce in this paper a filtering algorithm dedicated to this problem. The main idea is to label every node with respect to its relationships with other nodes of the graph, and to define a partial order on these labels in order to express compatibility of labels for subgraph isomorphism. This partial order over labels is used to filter domains. Labelings can also be strengthened by adding information from the labels of the neighbors. Such a strengthening can be applied iteratively until a fixpoint is reached. Practical experiments illustrate that our new filtering approach is more effective on difficult instances of scale free graphs than state-of-the-art algorithms and other CP approaches.

The Berth Allocation and Quay Crane Assignment Problem Using a CP Approach

This paper considers the combination of berth and crane allocation problems in container terminals. We propose a novel approach based on constraint programming which is able to model many realistic operational constraints. The costs for berth allocation, crane allocation, time windows, breaks and transition times during gang movements are optimized simultaneously. The model is based on a resource view where gangs are consumed by vessel activities. Side constraints are added independently around this core model. The model is richer than the state of the art in the operations research community. Experiments show that the model produces solutions with a cost gap of 1/10 (7,8%) to 1/5 (18,8%) compared to an ideal operational setting where operational constraints are ignored.

Six Ways of Integrating Symmetries within Non-overlapping Constraints

This paper introduces six ways for handling a chain of lexicographic ordering (lex-chain) constraint between the origins of identical orthotopes (e.g., rectangles, boxes, hyper-rectangles) subject to the fact that they should not pairwise overlap. While the first two ways deal with the integration of a lex-chain constraint within a generic geometric constraint kernel, the four latter ways deal with the conjunction of a lex-chain constraint and a non-overlapping or a cumulative constraint. Experiments on academic two and three dimensional placement problems as well as on industrial problems show the benefit of such a strong integration of symmetry breaking constraints and non-overlapping ones.

Combining Two Structured Domains for Modeling Various Graph Matching Problems

Graph pattern matching is a central application in many fields. In various areas, the structure of the pattern can only be approximated and exact matching is then too accurate. We focus here on approximations declared by the user within the pattern (optional nodes and forbidden arcs), covering graph/subgraph mono/isomorphism problems. In this paper, we show how the integration of two domains of computation over countable structures, graphs and maps , can be used for modeling and solving various graph matching problems from the simple graph isomorphism to approximate graph matching. To achieve this, we extend map variables allowing the domain and range to be non-fixed and constrained. We describe how such extended maps are designed then realized on top of finite domain and finite set variables with specific propagators. We show how a single monomorphism constraint is sufficient to model and solve those multiples graph matching problems. Furthermore, our experimental results show that our CP approach is competitive with a state of the art algorithm for subgraph isomorphism.

Principles and Practice of Constraint Programming

This paper considers the combination of berth and crane allocation problems in container terminals. We propose a novel approach based on constraint programming which is able to model many realistic operational constraints. The costs for berth allocation, crane allocation, time windows, breaks and transition times during gang movements are optimized simultaneously. The model is based on a resource view where gangs are consumed by vessel activities. Side constraints are added independently around this core model. The model is richer than the state of the art in the operations research community. Experiments show that the model produces solutions with a cost gap of 1/10 (7,8%) to 1/5 (18,8%) compared to an ideal operational setting where operational constraints are ignored.