This paper explores the application of Maximum Satisfiability (Max-SAT) to the complex problem of conference session scheduling, with a particular focus on minimizing working-group conflicts within the context of the ROADEF conference, the largest French-speaking event aimed at bringing together researchers from various fields such as combinatorial optimization and operational research. A Max-SAT model is introduced then enhanced with new variables, and solved through state-of-the-art solvers. The results of applying our formulation to data from ROADEF demonstrate its ability to effectively compute session schedules, while enabling to reduce the number of conflicts and the maximum number of parallel sessions compared to the handmade solutions proposed by the organizing committees. These findings underscore the potential of Max-SAT as a valuable tool for optimizing conference scheduling processes, offering a systematic and efficient solution that ensures a smoother and more productive experience for attendees and organizers alike.

The Minimum Sum Coloring Problem (MSCP) is an NP-Hard problem derived from the graph coloring problem (GCP) and has practical applications in different domains such as VLSI design, distributed resource allocation, and scheduling. There exist few exact solutions for MSCP, probably due to its search space much more elusive than that of GCP. On the contrary, much effort is spent in the literature to develop upper and lower bounds for MSCP. In this paper, we borrow a notion called motif, that was used in a recent work for upper bounding the minimum number of colors in an optimal solution of MSCP, to develop a new algebraic lower bound called for MSCP. Experiments on standard benchmarks for MSCP and GCP show that this new lower bound is substantially better than the existing lower bounds for several families of graphs.

We present a network decomposition method using binary decision diagrams (BDD), a state-of-the-art data structure to encode, and manipulate Boolean functions, for computing the reliability of networks such as computer, communication, or power networks. We consider the K-terminal reliability measure RK, which is defined as the probability that a subset K of nodes can communicate with each other, taking into account the possible failures of the network links. We present an exact algorithm for computing the if-terminal reliability of a network with perfect vertices in O(m.Fmax.2Fmax.BFmax), where BFmaxis the Bell number of the maximum boundary set of vertices Fmax, and m is the number of network links. Several examples, and experiments show the effectiveness of this approach.