Related papers: Maximum Matching and Linear Programming in Fixed-P…
We establish a linear programming formulation for the solution of joint chance constrained optimal control problems over finite time horizons. The joint chance constraint may represent an invariance, reachability or reach-avoid…
A geometric graph is a graph whose vertex set is a set of points in the plane and whose edge set contains straight-line segments. A matching in a graph is a subset of edges of the graph with no shared vertices. A matching is called perfect…
Motivated by the quest for a logic for PTIME and recent insights that the descriptive complexity of problems from linear algebra is a crucial aspect of this problem, we study the solvability of linear equation systems over finite groups and…
Given a graph $G=(V,E)$ with two distinguished vertices $s,t\in V$ and an integer $L$, an {\em $L$-bounded flow} is a flow between $s$ and $t$ that can be decomposed into paths of length at most $L$. In the {\em maximum $L$-bounded flow…
We design a fully polynomial time approximation scheme (FPTAS) for counting the number of matchings (packings) in arbitrary 3-uniform hypergraphs of maximum degree three, referred to as $(3,3)$-hypergraphs. It is the first polynomial time…
Consider a set of labels $L$ and a set of trees ${\mathcal T} = \{{\mathcal T}^{(1), {\mathcal T}^{(2), ..., {\mathcal T}^{(k) \$ where each tree ${\mathcal T}^{(i)$ is distinctly leaf-labeled by some subset of $L$. One fundamental problem…
The theoretical models providing mathematical abstractions for several significant optimization problems in machine learning, combinatorial optimization, computer vision and statistical physics have intrinsic similarities. We propose a…
We study fundamental graph problems such as graph connectivity, minimum spanning forest (MSF), and approximate maximum (weight) matching in a distributed setting. In particular, we focus on the Adaptive Massively Parallel Computation (AMPC)…
The article proposes an n-dimensional mathematical model of the visual representation of a linear programming problem. This model makes it possible to use artificial neural networks to solve multidimensional linear optimization problems,…
In this paper we study a scheduling problem arising from executing numerical simulations on HPC architectures. With a constant number of parallel machines, the objective is to minimize the makespan under memory constraints for the machines.…
Given a graph $G=(V, E)$, a connected sides cut $(U, V\backslash U)$ or $\delta (U)$ is the set of edges of E linking all vertices of U to all vertices of $V\backslash U$ such that the induced subgraphs $G[U]$ and $G[V\backslash U]$ are…
In this paper we present an algorithmic framework for solving a class of combinatorial optimization problems on graphs with bounded pathwidth. The problems are NP-hard in general, but solvable in linear time on this type of graphs. The…
Linear programming is a powerful method in combinatorial optimization with many applications in theory and practice. For solving a linear program quickly it is desirable to have a formulation of small size for the given problem. A useful…
Graph polynomials which are definable in Monadic Second Order Logic (MSOL) on the vocabulary of graphs are Fixed-Parameter Tractable (FPT) with respect to clique-width. In contrast, graph polynomials which are definable in MSOL on the…
Probabilistic Programming Languages (PPLs) allow users to encode statistical inference problems and automatically apply an inference algorithm to solve them. Popular inference algorithms for PPLs, such as sequential Monte Carlo (SMC) and…
The maximization for the independence systems defined on graphs is a generalization of combinatorial optimization problems such as the maximum $b$-matching, the unweighted MAX-SAT, the matchoid, and the maximum timed matching problems. In…
It is well-known that every maximal planar graph has a matching of size at least $\tfrac{n+8}{3}$ if $n\geq 14$. In this paper, we investigate similar matching-bounds for maximal \emph{1-planar} graphs, i.e., graphs that can be drawn such…
The present paper is devoted to studying of minimal parametric fillings of finite metric spaces (a version of optimal connection problem) by methods of Linear Programming. The estimate on the multiplicity of multi-tours appearing in the…
Learning to optimize is a rapidly growing area that aims to solve optimization problems or improve existing optimization algorithms using machine learning (ML). In particular, the graph neural network (GNN) is considered a suitable ML model…
Detectability of failures of linear programming (LP) decoding and its potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the LP problem. In this paper, we make a…