Related papers: Solving MaxSAT with Matrix Multiplication
We analyze to what extent the random SAT and Max-SAT problems differ in their properties. Our findings suggest that for random $k$-CNF with ratio in a certain range, Max-SAT can be solved by any SAT algorithm with subexponential slowdown,…
In this paper we consider non-smooth convex optimization problems with (possibly) infinite intersection of constraints. In contrast to the classical approach, where the constraints are usually represented as intersection of simple sets,…
We present MADAM, a parallel semidefinite based exact solver for Max-Cut, a problem of finding the cut with maximum weight in a given graph. The algorithm uses branch and bound paradigm that applies alternating direction method of…
The simple assembly line balancing problem (SALBP) concerns the assignment of tasks with pre-defined processing times to work stations that are arranged in a line. Hereby, precedence constraints between the tasks must be respected. The…
Boolean Satisfiability (SAT) is arguably the archetypical NP-complete decision problem. Progress in SAT solving algorithms has motivated an ever increasing number of practical applications in recent years. However, many practical uses of…
The Maximum Cut (MaxCut) problem is NP-Complete, and obtaining its optimal solution is NP-hard in the worst case. As a result, heuristic-based algorithms are commonly used, though their design often requires significant domain expertise.…
This paper presents a novel algorithm integrating global and robust optimization methods to solve continuous non-convex quadratic problems under convex uncertainty sets. The proposed Robust spatial branch-and-bound (RsBB) algorithm combines…
Restricted Boltzmann Machine (RBM) is a particular type of random neural network models modeling vector data based on the assumption of Bernoulli distribution. For multi-dimensional and non-binary data, it is necessary to vectorize and…
We present a batch trajectory optimizer that can simultaneously solve hundreds of different instances of the problem in real-time. We consider holonomic robots but relax the assumption of circular base footprint. Our main algorithmic…
The Exact Satisfiability problem, XSAT, is defined as the problem of finding a satisfying assignment to a formula $\varphi$ in CNF such that exactly one literal in each clause is assigned to be "1" and the other literals in the same clause…
Estimation of Distribution Algorithms (EDAs) require flexible probability models that can be efficiently learned and sampled. Restricted Boltzmann Machines (RBMs) are generative neural networks with these desired properties. We integrate an…
This paper considers the joint precoder design problem for multiple-input single-output (MISO) systems with coordinated base stations (BSs). We consider maximization of the total sum rate with per BS antenna power constraint problem. For…
Determinant maximization provides an elegant generalization of problems in many areas, including convex geometry, statistics, machine learning, fair allocation of goods, and network design. In an instance of the determinant maximization…
The problem of non-monotone $k$-submodular maximization under a knapsack constraint ($\kSMK$) over the ground set size $n$ has been raised in many applications in machine learning, such as data summarization, information propagation, etc.…
Despite having various attractive qualities such as high prediction accuracy and the ability to quantify uncertainty and avoid over-fitting, Bayesian Matrix Factorization has not been widely adopted because of the prohibitive cost of…
We develop a message-passing algorithm for noisy matrix completion problems based on matrix factorization. The algorithm is derived by approximating message distributions of belief propagation with Gaussian distributions that share the same…
Understanding the results of deep neural networks is an essential step towards wider acceptance of deep learning algorithms. Many approaches address the issue of interpreting artificial neural networks, but often provide divergent…
Constrained decision-making is essential for designing safe policies in real-world control systems, yet simulated environments often fail to capture real-world adversities. We consider the problem of learning a policy that will maximize the…
We give a general method of construting quantum circuit for random \QTR{it}{satisfiability} (SAT) problems with the basic logic gates such as multi-qubit controlled-NOT and NOT gates. The sizes of these circuits are almost the same as the…
Path planning for multiple robots (MRPP) represents a task of finding non-colliding paths for robots through which they can navigate from their initial positions to specified goal positions. The problem is usually modeled using undirected…