Related papers: Solving Projected Model Counting by Utilizing Tree…
We present a parallel algorithm for computing the treewidth of a graph on a GPU. We implement this algorithm in OpenCL, and experimentally evaluate its performance. Our algorithm is based on an $O^*(2^{n})$-time algorithm that explores the…
This paper proposes a new sampling-based nonlinear model predictive control (MPC) algorithm, with a bound on complexity quadratic in the prediction horizon N and linear in the number of samples. The idea of the proposed algorithm is to use…
We propose a unifying dynamic-programming framework to compute exact literal-weighted model counts of formulas in conjunctive normal form. At the center of our framework are project-join trees, which specify efficient project-join orders to…
The problem of deciding the validity (QSAT) of quantified Boolean formulas (QBF) is a vivid research area in both theory and practice. In the field of parameterized algorithmics, the well-studied graph measure treewidth turned out to be a…
It is well known that many local graph problems, like Vertex Cover and Dominating Set, can be solved in 2^{O(tw)}|V|^{O(1)} time for graphs G=(V,E) with a given tree decomposition of width tw. However, for nonlocal problems, like the…
Dynamic programming is a powerful technique that is, unfortunately, often inherently sequential. That is, there exists no unified method to parallelize algorithms that use dynamic programming. In this paper, we attempt to address this issue…
Many clustering applications in machine learning and data mining rely on solving metric-constrained optimization problems. These problems are characterized by $O(n^3)$ constraints that enforce triangle inequalities on distance variables…
This paper presents a new approach to solve linear and nonlinear model predictive control (MPC) problems that requires small memory footprint and throughput and is particularly suitable when the model and/or controller parameters change at…
We consider the well-studied problem of finding a spanning tree with minimum average distance between vertex pairs (called a MAD tree). This is a classic network design problem which is known to be NP-hard. While approximation algorithms…
We investigate the parameterized complexity of the Isometric Path Partition problem when parameterized by the treewidth ($\mathrm{tw}$) of the input graph, arguably one of the most widely studied parameters. Courcelle's theorem shows that…
We consider a weighted counting problem on matchings, denoted $\textrm{PrMatching}(\mathcal{G})$, on an arbitrary fixed graph family $\mathcal{G}$. The input consists of a graph $G\in \mathcal{G}$ and of rational probabilities of existence…
In this work, we introduce TreeWidzard, an engine for developing dynamic programming algorithms that decide graph-theoretic properties parameterized by treewidth and pathwidth. Besides providing a unified framework for algorithms deciding…
Decompositional parameters such as treewidth are commonly used to obtain fixed-parameter algorithms for NP-hard graph problems. For problems that are W[1]-hard parameterized by treewidth, a natural alternative would be to use a suitable…
In this paper we propose, implement, and test the first practical decomposition algorithms for the width parameters treecut width and treedepth. These two parameters have recently gained a lot of attention in the theoretical research…
We outline a new approach for solving optimization problems which enforce triangle inequalities on output variables. We refer to this as metric-constrained optimization, and give several examples where problems of this form arise in machine…
We investigate the complexity of several fundamental polynomial-time solvable problems on graphs and on matrices, when the given instance has low treewidth; in the case of matrices, we consider the treewidth of the graph formed by non-zero…
The Weighted First-Order Model Counting Problem (WFOMC) asks to compute the weighted sum of models of a given first-order logic sentence over a given domain. Conditioning WFOMC on evidence -- fixing the truth values of a set of ground…
Monte Carlo methods are widely used for approximating complicated, multidimensional integrals for Bayesian inference. Population Monte Carlo (PMC) is an important class of Monte Carlo methods, which utilizes a population of proposals to…
Treewidth is a useful tool in designing graph algorithms. Although many NP-hard graph problems can be solved in linear time when the input graphs have small treewidth, there are problems which remain hard on graphs of bounded treewidth. In…
Fixed parameter tractable algorithms for bounded treewidth are known to exist for a wide class of graph optimization problems. While most research in this area has been focused on exact algorithms, it is hard to find decompositions of…