Robustness, stability, recoverability, and reliability in constraint satisfaction problems

Abstract

Abstract. Many real-world problems in Artificial Intelligence (AI) as well as in other areas of computer science and engineering can be efficiently modeled and solved using constraint programming techniques. In many real-world scenarios the problem is partially known, imprecise and dynamic such that some effects of actions are undesired and/or several un-foreseen incidences or changes can occur. Whereas expressivity, efficiency and optimality have been the typical goals in the area, there are several issues regarding robustness that have a clear relevance in dynamic Constraint Satisfaction Problems (CSP). However, there is still no clear and common definition of robustness-related concepts in CSPs. In this paper, we propose two clearly differentiated definitions for robustness and stability in CSP solutions. We also introduce the concepts of recoverability and reliability, which arise in temporal CSPs. All these definitions are based on related well-known concepts, which are addressed in engineering and other related areas.

Clustering-based fragmentation and data replication for flexible query answering in distributed databases

“…Regarding the update problem, we plan to apply a special optimization approach to database replication: the notion of recovery robust optimization [32] describes optimization methods that compute a solution that can later on adapt to changing conditions which so far have been used mostly for timetabling applications [33] or job sequencing [8] or telecommunication networks [34]; in this respect it is important to ensure a worst case guarantee as in [8]. This is a different approach than presented here and its implications will hence be the topic of future work.…”

Complexity Study for the Robust Stable Marriage Problem

“…Table 3: The list of all stable matchings for the instance given in Table 1. (2,5), (3,7), (4,4), (5,2), (6, 1), (7, 3)} (2,5), (3,7), (4,4), (5,2), (6, 1), (7, 6)} (2,6), (3,7), (4,4), (5,2), (6, 5), (7, 1)} (2,6), (3,1), (4,4), (5,2), (6, 5), (7, 7)} (2,4), (3, 1), (4, 6), (5, 2), (6, 5), (7, 7)} (2,6), (3,7), (4,4), (5,2), (6, 3), (7, 1)} (2,4), (3, 1), (4, 6), (5, 2), (6, 3), (7, 7)} (2,6), (3,7), (4,<...>…”

“…Also note that, this example instance is one of the smallest that can be created respecting the rules of the SAT-SM. (1, 4) l 3 (3, 4) l 4 (3, 5) l 5 (5, 6) l 6 (2, 6) Table 6: Clauses of the SAT-SM instance given in Table 5.…”

“…The instance I F contains two fixed men (m 2 and m 6 ) and 12 stable matchings. Only one stable match-ing, namely M = { (1,8), (2,5), (3,6), (4, 3), (5, 7), (6, 1), (7,2), (8,4)}, is a (1, 1)-supermatch. The closed subset corresponding to M is S = {ρ 0 , ρ 1 , ρ 3 }.…”

“…We find in the literature a variety of definitions of robustness depending on the context, for example in scheduling and timetabling [22], constraint programming [3], machine learning [26], and economics [25]. Some researchers define a solution to be robust if it remains a solution after an unexpected occurrence of an event.…”