We study the notion of robustness in stable matching problems. We first define robustness by introducing (a, b)-supermatches. An (a, b)-supermatch is a stable matching in which if a pairs break up it is possible to find another stable matching by changing the partners of those a pairs and at most b other pairs. In this context, we define the most robust stable matching as a (1, b)-supermatch where b is minimum. We show that checking whether a given stable matching is a (1, b)-supermatch can be done in polynomial time. Next, we use this procedure to design a constraint programming model, a local search approach, and a genetic algorithm to find the most robust stable matching. Our empirical evaluation on large instances show that local search outperforms the other approaches.

Summary— Possible interactions between an infection with Ophiostoma querci and water stress on pedunculate oak (Quercus robur) were tested with potted saplings. O querci was inoculated into the stems of 3-year-old saplings, and a severe drought was imposed for about 40 d. Drought promoted an irreversible decline in total leaf specific conductance of all saplings; direct measurement of losses of hydraulic conductivity in twigs and petioles revealed that a strong embolization occurred in the vessels as soon as minimal leaf water potential decreased below -2.5 MPa. This vulnerability to cavitation on rooted seedlings was in agreement with earlier data obtained on cut branches from the same species left to freely dehydrate; a slight artifact was probably due to the onset of occlusions of embolised vessels in the rooted plants. The presence of fungal spores in the stems did not induce any modification in these water relations on well-watered or stressed seedlings.

International audienceThe problem presented in this paper is a generalization of the usual coupled-tasks scheduling problem in presence of compatibility constraints. The reason behind this study is the data acquisition problem for a submarine torpedo. We investigate a particular configuration for coupled tasks (any task is divided into two sub-tasks separated by an idle time), in which the idle time of a coupled task is equal to the sum of durations of its two sub-tasks. We prove -completeness of the minimization of the schedule length, we show that finding a solution to our problem amounts to solving a graph problem, which in itself is close to the minimum-disjoint-path cover (min-DCP) problem. We design a (3a+2b)/(2a+2b)-approximation, where a and b (the processing time of the two sub-tasks) are two input data such as a>b>0, and that leads to a ratio between 3/2 and 5/4. Using a polynomial-time algorithm developed for some class of graph of min-DCP, we show that the ratio decreases to 1.37

The Robust Stable Marriage problem (RSM) is a variant of the classic Stable Marriage problem in which the robustness of a given stable matching is measured by the number of modifications required to find an alternative stable matching should some pairings break due to an unforeseen event. We focus on the complexity of finding an (a, b)-supermatch. An (a, b)-supermatch is defined as a stable matching in which if any a (non-fixed) men/women break up it is possible to find another stable matching by changing the partners of those a men/women and the partners of at most b others. We first discuss a model based on independent sets for finding (1, 1)-supermatches. Secondly, in order to show that deciding whether or not there exists a (1, b)-supermatch is N P-complete, we first introduce a SAT formulation for which the decision problem is N P-complete by using Schaefer's Dichotomy Theorem. We then show the equivalence between this SAT formulation and finding a (1, 1)supermatch on a specific family of instances. We also focus on studying the threshold between the cases in P and N P-complete for this problem.

The Rosetta/Philae mission was launched in 2004 by the European Space Agency (ESA). It is scheduled to reach the comet 67P/Churyumov-Gerasimenko in November 2014 after traveling more than six billion kilometers. The Philae module will then be separated from the orbiter (Rosetta) to attempt the first ever landing on the surface of a comet. If it succeeds, it will engage a sequence of scientific exploratory experiments on the comet. In this paper, we describe a constraint programming model for scheduling the different experiments of the mission. A feasible plan must satisfy a number of constraints induced by energetic resources, precedence relations on tasks, and incompatibility between instruments. Moreover, a very important aspect is related to the transfer (to the orbiter then to the Earth) of all the data produced by the instruments. The capacity of inboard memories and the limitation of transfers within visibility windows between lander and orbiter, make the transfer policy implemented on the lander CPU prone to data loss. We introduce a global constraint to handle data transfers. The purpose of this constraint is to ensure that data-producing tasks are scheduled in such a way that no data is lost. Thanks to this constraint and to the filtering rules we propose, mission control is now able to compute feasible plans in a few seconds for scenarios where minutes were previously often required. Moreover, in many cases, data transfers are now much more accurately simulated, thus increasing the reliability of the plans.

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This paper considers a special case of the coupled-tasks scheduling problem on one processor. The general problems were analyzed in depth by Orman and Potts [1]. In this paper, we consider that all processing times are equal to 1, the gap has exact length L, we have precedence constraints, compatibility constraints are introduced and the criterion is to minimize the scheduling length. We use this problem to study the problem of data acquisition and data treatment of a torpedo under the water. We show that this problem is N P-complete and we propose an ρ-approximation algorithm where ρ ≤ (L+6) 6 .

Abstract. We consider the makespan minimization coupled-tasks problem in presence of compatibility constraints with a specified topology. In particular, we focus on stretched coupled-tasks, i.e. coupled-tasks having the same sub-tasks execution time and idle time duration. We study several problems in framework of classic complexity and approximation for which the compatibility graph is bipartite (star, chain, . . .).In such a context, we design some efficient polynomial-time approximation algorithms for an intractable scheduling problem according to some parameters.