Related papers: Exponentially faster fixed-parameter algorithms fo…
In this paper, we propose iterative inner/outer approximations based on a recent notion of block factor-width-two matrices for solving semidefinite programs (SDPs). Our inner/outer approximating algorithms generate a sequence of upper/lower…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
We give a strongly polynomial-time algorithm for integer linear programs defined by integer coefficient matrices whose subdeterminants are bounded by a constant and that contain at most two nonzero entries in each row. The core of our…
We introduce a variation of the scheduling with precedence constraints problem that has applications to molecular folding and production management. We are given a bipartite graph $H=(B,S)$. Vertices in $B$ are thought of as goods or…
We present the first near optimal approximation schemes for the maximum weighted (uncapacitated or capacitated) $b$--matching problems for non-bipartite graphs that run in time (near) linear in the number of edges. For any…
We give an approximation algorithm for packing and covering linear programs (linear programs with non-negative coefficients). Given a constraint matrix with n non-zeros, r rows, and c columns, the algorithm computes feasible primal and dual…
In this paper we consider the problem of scheduling on parallel machines with a presence of incompatibilities between jobs. The incompatibility relation can be modeled as a complete multipartite graph in which each edge denotes a pair of…
This paper presents fast first-order methods for solving linear programs (LPs) approximately. We adapt online linear programming algorithms to offline LPs and obtain algorithms that avoid any matrix multiplication. We also introduce a…
We study the design of fixed-parameter algorithms for problems already known to be solvable in polynomial time. The main motivation is to get more efficient algorithms for problems with unattractive polynomial running times. Here, we focus…
In the number partitioning problem (NPP) one aims to partition a given set of $N$ real numbers into two subsets with approximately equal sum. The NPP is a well-studied optimization problem and is famous for possessing a…
In many applications including integer-forcing linear multiple-input and multiple-output (MIMO) receiver design, one needs to solve a successive minima problem (SMP) on an $n$-dimensional lattice to get an optimal integer coefficient matrix…
Packing and covering linear programs belong to the narrow class of linear programs that are efficiently solvable in parallel and distributed models of computation, yet are a powerful modeling tool for a wide range of fundamental problems in…
We study the problem of scheduling a general computational DAG on multiple processors in a 2-level memory hierarchy. This setting is a natural generalization of several prominent models in the literature, and it simultaneously captures…
We present new, faster pseudopolynomial time algorithms for the $k$-Subset Sum problem, defined as follows: given a set $Z$ of $n$ positive integers and $k$ targets $t_1, \ldots, t_k$, determine whether there exist $k$ disjoint subsets…
In this work, we develop an adaptive, multivariate partitioning algorithm for solving mixed-integer nonlinear programs (MINLP) with multi-linear terms to global optimality. This iterative algorithm primarily exploits the advantages of…
Current algorithms for large-scale industrial optimization problems typically face a trade-off: they either require exponential time to reach optimal solutions, or employ problem-specific heuristics. To overcome these limitations, we…
A robust algorithm for non-negative matrix factorization (NMF) is presented in this paper with the purpose of dealing with large-scale data, where the separability assumption is satisfied. In particular, we modify the Linear Programming…
The class $(r,2)$-CSP, or simply Max 2-CSP, consists of constraint satisfaction problems with at most two $r$-valued variables per clause. For instances with $n$ variables and $m$ binary clauses, we present an $O(n r^{5+19m/100})$-time…
There is an increasing need for algorithms that can accurately detect changepoints in long time-series, or equivalent, data. Many common approaches to detecting changepoints, for example based on penalised likelihood or minimum description…
We study the problem of multiway number partition optimization, which has a myriad of applications in the decision, learning and optimization literature. Even though the original multiway partitioning problem is NP-hard and requires…