We study the problem of partitioning a graph into k connected components, which may also be referred to as the maximum k-cutset problem. Firstly, we present an exact algorithm and a variant, both implemented as integer linear programming (ILP) models. We then present a heuristic approach that will be seen to be extremely competitive with the exact algorithm for the ranges of graph under consideration.

In this paper, we consider the two-parallel machine scheduling problem with a non-availability interval. We aim to minimize the maximum lateness when every job has a positive tail. We show that the problem has a constant polynomial approximation algorithm. We present a dynamic programming algorithm and we show that the problem has an FPTAS (Fully Polynomial Time Approximation Algorithm). The proposed FPTAS has a strongly polynomial running time. Finally, we present some numerical experiments and we analyze the obtained results.

In this paper, we present a genetic algorithm for the open shop scheduling problem. We use a simple and efficient chromosome representation based on the job's occurrence and the fitness function reflect the length of the schedule. The solutions obtained after performing the different operators of the genetic algorithm are always feasible. Heuristic approaches are also developed to generate the initial population and to improve the obtained solutions. The algorithm was implemented and computational results show interesting result.

In this paper, we consider the bipartite complete matching vertex interdiction problem, taking into account some incompatibilities existing among the resources to assign. This problem ensures the obtainment of a robust assignment, which is defined by the number of missing resources still allowing a valid assignment. We introduce graph formulations, considering a single time period or several ones. This problem is shown to be NP-hard, even when considering only a single time period. For several time periods, we adapt the graph formulation, allowing us to solve the problem using polynomial heuristics. Two greedy algorithms and a genetic algorithm are proposed and compared on a randomly-generated testbed.

In this paper, we consider the Robust Nurse Assignment Problem. This consists in finding the maximum number of absences of qualified nurses still permitting an optimal treatment of patients, leading us to the notion of critical jobs. We introduce the Bipartite Complete Matching Vertex Interdiction Problem as the graph formulation of this problem. We show that it can be solved in polynomial time thanks to the integer polytope of an associated sub-problem. Then, we study the polytope associated with the Bipartite Complete Matching Vertex Interdiction Problem. We also extend the well-known Hall theorem to this problem.

Markov decision processes (MDP) have been widely used as a framework for planning under uncertainty. They allow to compute optimal sequences of actions in order to achieve a given goal, accounting for actuator uncertainties. But algorithms classically used to solve MDPs are intractable for problems requiring a large state space. Plans are computed considering the whole state space, without using any knowledge about the initial state of the problem. We propose a new technique to build partial plans for a mobile robot, considering only a restricted MDP which contains a small set of states composing a path between the initial state and the goal state. To ensure good quality of the solution, the path has to be very similar to the one which would have been computed on the whole environment. We present a new method to compute partial plans, showing that representing the environment as a directed graph can be very helpful to find near-optimal paths. Partial plans obtained using this method are very similar to complete plans, and computing times are considerably reduced.

Markov decision processes have been successfully used in robotics for indoor robot navigation problems. They allow the computation of optimal sequences of actions in order to achieve a given goal, accounting for actuator uncertainties. However, MDPs are unsatisfactory at avoiding unknown obstacles. On the other hand, reactive navigators are particularly adapted to that, and don't need any prior knowledge about the environment, but they are unable to plan the set of actions that will permit the realization of a given mission. We present a new state aggregation technique for Markov decision processes, such that part of the work usually dedicated to the planner is achieved by a reactive navigator. Thus some characteristics of our environments, such as the width of corridors, have not been considered, which allows to cluster states together, significantly reducing the state space. As a consequence, policies are computed faster and are shown to be at least as efficient as optimal ones.

We present a new method to localize a mobile robot in dynamic environments. This method is based on place recognition, and a match between places recognized and the sequence of places that the mobile robot is able to see during a run from an initial place to an ending place. Our method gives a coarse idea of the robot's position and orientation. Moreover, the robot can determine the actual state of places (i.e. open doors, closed doors).

In this paper we present two state aggregation methods used to build stochastic plans, modelling our environment with Markov decision processes. Classical methods used to compute stochastic plans are highly intractable for problems necessitating a large number of states, such as our robotics application. The use of aggregation techniques allows to reduce the number of states and our methods give nearly optimal plans in a significantly reduced time.

This paper describes the Time Warp Operating System, under development for three years at the Jet Propulsion Laboratory for the Caltech Mark III Hypercube multi-processor. Its primary goal is concurrent execution of large, irregular discrete event simulations at maximum speed. It also supports any other distributed applications that are synchronized by virtual time.