Related papers: Semidefinite Programming in Timetabling and Mutual…
Graph coloring is one of the most famous computational problems with applications in a wide range of areas such as planning and scheduling, resource allocation, and pattern matching. So far coloring problems are mostly studied on static…
Given a linear ordering of the vertices of a graph, the cutwidth of a vertex $v$ with respect to this ordering is the number of edges from any vertex before $v$ (including $v$) to any vertex after $v$ in this ordering. The cutwidth of an…
We consider the problem of scheduling a set of $n$ tasks on $m$ processors under precedence, communication, and global system energy constraints to minimize makespan. We extend existing scheduling models to account for energy usage and give…
Dynamic Programming (DP) and Constraint Programming (CP) are well-established paradigms for solving combinatorial optimization problems. Usually, these two approaches are used separately. This paper aims to show that the two can be combined…
This paper presents the Lagrangian duality theory for mixed-integer semidefinite programming (MISDP). We derive the Lagrangian dual problem and prove that the resulting Lagrangian dual bound dominates the bound obtained from the continuous…
Finding actions that satisfy the constraints imposed by both external inputs and internal representations is central to decision making. We demonstrate that some important classes of constraint satisfaction problems (CSPs) can be solved by…
Robots are becoming an increasingly common part of scientific work within laboratory environments. In this paper, we investigate the problem of designing \emph{schedules} for completing a set of tasks at fixed locations with multiple robots…
We consider the global optimization of nonconvex mixed-integer quadratic programs with linear equality constraints. In particular, we present a new class of convex quadratic relaxations which are derived via quadratic cuts. To construct…
The Promise Constraint Satisfaction Problem (PCSP) is a recently introduced vast generalization of the Constraint Satisfaction Problem (CSP). We investigate the computational complexity of a class of PCSPs beyond the most studied cases -…
De Klerk, Pasechnik, and Sotirov give a semidefinite programming constraint for the Traveling Salesman Problem (TSP) based on the matrix-tree Theorem. This constraint says that the aggregate weight of all spanning trees in a solution to a…
We consider optimization problems containing nonconvex quadratic functions for which semidefinite programming (SDP) relaxations often yield strong bounds. We investigate linear inequalities that outer approximate the positive semidefinite…
Resolving a conjecture of Abbe, Bandeira and Hall, the authors have recently shown that the semidefinite programming (SDP) relaxation of the maximum likelihood estimator achieves the sharp threshold for exactly recovering the community…
It has been recently proven that the semidefinite programming (SDP) relaxation of the optimal power flow problem over radial networks is exact under technical conditions such as not including generation lower bounds or allowing load…
We consider the uniform parallel machines scheduling problem in the context of optimistic bilevel optimization, where two speed options are considered. In this scenario, the leader aims to minimize the weighted number of tardy jobs, while…
Semidefinite programming is an important tool to tackle several problems in data science and signal processing, including clustering and community detection. However, semidefinite programs are often slow in practice, so speed up techniques…
We consider a natural extension of online makespan scheduling on identical parallel machines by introducing scenarios. A scenario is a subset of jobs, and the task of our problem is to find a global assignment of the jobs to machines so…
Task graphs have been studied for decades as a foundation for scheduling irregular parallel applications and incorporated in programming models such as OpenMP. While many high-performance parallel libraries are based on task graphs, they…
The graph bisection problem is the problem of partitioning the vertex set of a graph into two sets of given sizes such that the sum of weights of edges joining these two sets is optimized. We present a semidefinite programming relaxation…
We deal with a challenging scheduling problem on parallel machines with sequence-dependent setup times and release dates from a real-world application of semiconductor work-shop production. There, jobs can only be processed by dedicated…
In this paper the problem of scheduling of jobs on parallel machines under incompatibility relation is considered. In this model a binary relation between jobs is given and no two jobs that are in the relation can be scheduled on the same…