A Partial Taxonomy of Substitutability and Interchangeability

Substitutability, interchangeability and related concepts in Constraint Programming were introduced approximately twenty years ago and have given rise to considerable subsequent research. We survey this work, classify, and relate the different concepts, and indicate directions for future work, in particular with respect to making connections with research into symmetry breaking. This paper is a condensed version of a larger work in progress.Comment: 18 pages, The 10th International Workshop on Symmetry in Constraint Satisfaction Problems (SymCon'10

Proteus: A Hierarchical Portfolio of Solvers and Transformations

In recent years, portfolio approaches to solving SAT problems and CSPs have become increasingly common. There are also a number of different encodings for representing CSPs as SAT instances. In this paper, we leverage advances in both SAT and CSP solving to present a novel hierarchical portfolio-based approach to CSP solving, which we call Proteus, that does not rely purely on CSP solvers. Instead, it may decide that it is best to encode a CSP problem instance into SAT, selecting an appropriate encoding and a corresponding SAT solver. Our experimental evaluation used an instance of Proteus that involved four CSP solvers, three SAT encodings, and six SAT solvers, evaluated on the most challenging problem instances from the CSP solver competitions, involving global and intensional constraints. We show that significant performance improvements can be achieved by Proteus obtained by exploiting alternative view-points and solvers for combinatorial problem-solving.Comment: 11th International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. The final publication is available at link.springer.co

Comital Ireland, 1333–1534

The history of late-medieval Ireland is not exactly littered with dates that command general recognition, so it is surely suggestive that two which have achieved a degree of notoriety concern the fortunes, or rather misfortunes, of Ireland’s earls and earldoms: the murder of William Burgh, the ‘brown’ earl of Ulster, in 1333; and the rebellion in 1534 of Thomas Fitzgerald (‘Silken Thomas’), soon-to-be tenth earl of Kildare. These are dates of demarcation. In the broadest terms, 1333 has been understood to mark the end of the expansion of royal power under the Plantagenets, 1534 the start of its vigorous reassertion under the Tudors. What occurred between these chronological bookends? For Goddard Orpen (d. 1932), writing in 1920 when the Anglo-Irish tradition he cherished seemed imperilled by the prospect of Irish secession from the United Kingdom, the murder of the earl of Ulster in 1333 was a moment of dark, almost metonymic, significance: ‘the door was now closed on a century and a half of remarkable progress, vigour, and comparative order, and two centuries of retrogression, stagnation, and comparative anarchy were about to be ushered in’

Generalizing backdoors

Abstract. A powerful intuition in the design of search methods is that one wants to proactively select variables that simplify the problem instance as much as possible when these variables are assigned values. The notion of “Backdoor ” variables follows this intuition. In this work we generalize Backdoors in such a way to allow more general classes of sub-solvers, both complete and heuristic. In order to do so, Pseudo-Backdoors and Heuristic-Backdoors are formally introduced and then applied firstly to a simple Multiple Knapsack Problem and secondly to a complex combinatorial optimization problem in the area of stochastic inventory control. Our preliminary computational experience shows the effectiveness of these approaches that are able to produce very low run times and — in the case of Heuristic-Backdoors — high quality solutions by employing very simple heuristic rules such as greedy local search strategies.

Coalition Formation and Combinatorial Auctions; Applications to Self-organization and Self-management in Utility Computing

In this paper we propose a two-stage protocol for resource management in a hierarchically organized cloud. The first stage exploits spatial locality for the formation of coalitions of supply agents; the second stage, a combinatorial auction, is based on a modified proxy-based clock algorithm and has two phases, a clock phase and a proxy phase. The clock phase supports price discovery; in the second phase a proxy conducts multiple rounds of a combinatorial auction for the package of services requested by each client. The protocol strikes a balance between low-cost services for cloud clients and a decent profit for the service providers. We also report the results of an empirical investigation of the combinatorial auction stage of the protocol.Comment: 14 page