Related papers: Towards Effective Exact Algorithms for the Maximum…
This paper focuses on designing edge-weighted networks, whose robustness is characterized by maximizing algebraic connectivity, or the second smallest eigenvalue of the Laplacian matrix. This problem is motivated by cooperative vehicle…
The Schr\"odinger bridge problem (SBP) finds the most likely stochastic evolution between two probability distributions given a prior stochastic evolution. As well as applications in the natural sciences, problems of this kind have…
Optimal planning with respect to learned neural network (NN) models in continuous action and state spaces using mixed-integer linear programming (MILP) is a challenging task for branch-and-bound solvers due to the poor linear relaxation of…
Recent work has shown that it is possible to train deep neural networks that are provably robust to norm-bounded adversarial perturbations. Most of these methods are based on minimizing an upper bound on the worst-case loss over all…
Building on existing algorithms and results, we offer new insights and algorithms for various problems related to detecting maximal and maximum bicliques. Most of these results focus on graphs with small maximum degree, providing improved…
The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…
This paper addresses the problem of planning under uncertainty in large Markov Decision Processes (MDPs). Factored MDPs represent a complex state space using state variables and the transition model using a dynamic Bayesian network. This…
We propose an efficient algorithm for approximate computation of the profile maximum likelihood (PML), a variant of maximum likelihood maximizing the probability of observing a sufficient statistic rather than the empirical sample. The PML…
The NP-hard Maximum Planar Subgraph problem asks for a planar subgraph $H$ of a given graph $G$ such that $H$ has maximum edge cardinality. For more than two decades, the only known non-trivial exact algorithm was based on integer linear…
We investigate robust optimization problems defined for maximizing convex functions. For finite uncertainty set, we develop a geometric branch-and-bound algorithmic approach to solve this problem. The geometric branch-and-bound algorithm…
Recent advances in symbolic dynamic programming (SDP) combined with the extended algebraic decision diagram (XADD) data structure have provided exact solutions for mixed discrete and continuous (hybrid) MDPs with piecewise linear dynamics…
We present a first exact study on higher-dimensional packing problems with order constraints. Problems of this type occur naturally in applications such as logistics or computer architecture and can be interpreted as higher-dimensional…
Robust optimal or min-max model predictive control (MPC) approaches aim to guarantee constraint satisfaction over a known, bounded uncertainty set while minimizing a worst-case performance bound. Traditionally, these methods compute a…
We take an existing implementation of an algorithm for the maximum clique problem and modify it so that we can distribute it over an ad-hoc cluster of machines. Our goal was to achieve a significant speedup in performance with minimal…
The proximal bundle method (PBM) is a fundamental and computationally effective algorithm for solving nonsmooth optimization problems. In this paper, we present the first variant of the PBM for smooth objectives, achieving an accelerated…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
The submodular function maximization is an attractive optimization model that appears in many real applications. Although a variety of greedy algorithms quickly find good feasible solutions for many instances while guaranteeing…
Bi-quadratic programming over unit spheres is a fundamental problem in quantum mechanics introduced by pioneer work of Einstein, Schr\"odinger, and others. It has been shown to be NP-hard; so it must be solve by efficient heuristic…
We analyse the convergence of the proximal gradient algorithm for convex composite problems in the presence of gradient and proximal computational inaccuracies. We derive new tighter deterministic and probabilistic bounds that we use to…
This contribution extends the Bron Kerbosch algorithm for solving the maximum weight clique problem, where continuous-valued weights are assigned to both, vertices and edges. We applied the proposed algorithm to graph matching problems.