the Operations Research and Optimization team at Google develops both general purpose optimization tools and solutions for internal optimization problems. We will describe the tools – most of which are available at h...
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Given a sequence of variables X = 〈x 0, x 1, …, xn − 1 〉, we consider the IncreasingSum constraint, which imposes ∀ i ∈ [0, n − 2] xi ≤ xi + 1, and Σxi∈X xi = S. We propose an Θ(n) bound-consistency algorit...
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this paper revisits the tree constraint introduced in [2] which partitions the nodes of a n-nodes, m-arcs directed graph into a set of node-disjoint anti-arborescences for which only certain nodes can be tree roo...
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In this paper we describe a constraint Seeker application which provides a web interface to search for global constraints in the global constraint catalog, given positive and negative, fully instantiated (ground) exam...
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In this paper, we describe a constraintprogramming (cp) route finding application for a container transportation company. Mathematically, this amounts to finding the k shortest paths in a directed graph. However the ...
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Consistencies are properties of constraint networks that can be enforced by appropriate algorithms to reduce the size of the search space to be explored. Recently, many consistencies built upon taking decisions (most ...
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Many cumulative problems are such that the horizon is fixed and cannot be delayed. In this situation, it often occurs that all the activities cannot be scheduled without exceeding the capacity at some points in time. ...
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A depth-first search algorithm can be used to find optimal solutions of a constraint Satisfaction Problem (CSP) with respect to a set of conditional preferences statements (e.g., a cp-net). this involves checking at e...
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the presence of symmetries in a constraint satisfaction problem gives an opportunity for more efficient search. Within the class of matrix models, we show that the problem of deciding whether some well known permutati...
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We consider the impact of value ordering heuristics on the search effort required to find all solutions, or proving none exist, to a constraint satisfaction problem in k-way branching search. We show that when the var...
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