Related papers: FPT-algorithms for The Shortest Lattice Vector and…
Affine rank minimization problem is the generalized version of low rank matrix completion problem where linear combinations of the entries of a low rank matrix are observed and the matrix is estimated from these measurements. We propose a…
We introduce a novel approach of using important cuts which allowed us to design significantly faster fixed-parameter tractable (FPT) algorithms for the following routing problems: the Mixed Chinese Postman Problem parameterized by the…
Inspection planning is concerned with computing the shortest robot path to inspect a given set of points of interest (POIs) using the robot's sensors. This problem arises in a wide range of applications from manufacturing to medical…
Traditional lock-free parallel algorithms for combinatorial optimization problems, such as shortest paths, stable matching, and job scheduling require programmers to write problem-specific routines and synchronization code. We propose a…
Due to the limited connectivity of gate model quantum devices, logical quantum circuits must be compiled to target hardware before they can be executed. Often, this process involves the insertion of SWAP gates into the logical circuit,…
Given a graph $G=(V,E)$, the longest induced path problem asks for a maximum cardinality node subset $W\subseteq V$ such that the graph induced by $W$ is a path. It is a long established problem with applications, e.g., in network analysis.…
We present an approximation scheme for optimizing certain Quadratic Integer Programming problems with positive semidefinite objective functions and global linear constraints. This framework includes well known graph problems such as Minimum…
When solving multi-objective programs, the number of objectives essentially determines the computing time. This can even lead to practically unsolvable problems. Consequently, it is worthwhile to reduce the number of objectives without…
Given a graph $G=(V,E)$ with two distinguished vertices $s,t\in V$ and an integer parameter $L>0$, an {\em $L$-bounded cut} is a subset $F$ of edges (vertices) such that the every path between $s$ and $t$ in $G\setminus F$ has length more…
Due to their importance in practice, dominating set problems in graphs have been greatly studied in past and different formulations of these problems are presented in literature. This paper's focus is on two problems: weakly convex…
The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite…
In the Integer Quadratic Programming problem input is an n*n integer matrix Q, an m*n integer matrix A and an m-dimensional integer vector b. The task is to find a vector x in Z^n, minimizing x^TQx, subject to Ax <= b. We give a fixed…
Mixed-integer linear programming (MILP) is at the core of many advanced algorithms for solving fundamental problems in combinatorial optimization. The complexity of solving MILPs directly correlates with their support size, which is the…
In this paper, the problem of matrix rank minimization under affine constraints is addressed. The state-of-the-art algorithms can recover matrices with a rank much less than what is sufficient for the uniqueness of the solution of this…
We show that the Minimal Length-Bounded L-But problem can be computed in linear time with respect to L and the tree-width of the input graph as parameters. In this problem the task is to find a set of edges of a graph such that after…
Let F be a finite set of graphs. In the F-Deletion problem, we are given an n-vertex graph G and an integer k as input, and asked whether at most k vertices can be deleted from G such that the resulting graph does not contain a graph from F…
A classical problem in matrix computations is the efficient and reliable approximation of a given matrix by a matrix of lower rank. The truncated singular value decomposition (SVD) is known to provide the best such approximation for any…
The classic algorithm [Papadimitriou, J.ACM '81] for IPs has a running time $n^{O(m)}(m\cdot\max\{\Delta,\|\textbf{b}\|_{\infty}\})^{O(m^2)}$, where $m$ is the number of constraints, $n$ is the number of variables, and $\Delta$ and…
Approximate linear programming (ALP) is an efficient approach to solving large factored Markov decision processes (MDPs). The main idea of the method is to approximate the optimal value function by a set of basis functions and optimize…
A classic result of Lenstra [Math.~Oper.~Res.~1983] says that an integer linear program can be solved in fixed-parameter tractable (FPT) time for the parameter being the number of variables. We extend this result by incorporating…