Related papers: A compact implementation of a recently proposed st…
This article presents a numerical illustration of a recently proposed strongly polynomial-time algorithm for the general linear programming (LP) problem. Each iteration of the proposed algorithm consists of two Gauss-Jordan pivoting…
This article presents a validation of a recently proposed strongly polynomial-time algorithm for the general linear programming problem. The proposed algorithm is an implicit reduction procedure that combines primal and dual linear…
This article presents a strongly polynomial-time algorithm for the general linear programming problem. This algorithm is an implicit reduction procedure that works as follows. Primal and dual problems are combined into a special system of…
This article describes certain ratios that attend pairs of complementary Gauss-Jordan pivotings transforming skew-symmetric matrices. Our interest in those ratios was motivated by a need to prove a crucial Claim stated in a recently…
It is well known that the most challenging question in optimization and discrete geometry is whether there is a strongly polynomial time simplex algorithm for linear programs (LPs). This paper gives a positive answer to this question by…
A polynomial-time algorithm for 0-1 integer linear programmings has been proposed. This method continues the classic idea of solving ILP with its LP relaxation. The innovation is that every constraint in the LP is reconstructed into a…
Linear Programming (LP) is widely applied in industry and is a key component of various other mathematical problem-solving techniques. Recent work introduced an LP compiler translating polynomial-time, polynomial-space algorithms into…
We analyze the bit complexity of efficient algorithms for fundamental optimization problems, such as linear regression, $p$-norm regression, and linear programming (LP). State-of-the-art algorithms are iterative, and in terms of the number…
We study the general scheduling problem (GSP) which generalizes and unifies several well-studied preemptive single-machine scheduling problems, such as weighted flow time, weighted sum of completion time, and minimizing the total weight of…
In this paper, we propose a carefully optimized "half-gcd" algorithm for polynomials. We achieve a constant speed-up with respect to previous work for the asymptotic time complexity. We also discuss special optimizations that are possible…
In this paper we show how to combine two algorithmic techniques to obtain linear time algorithms for various optimization problems on graphs, and present a subroutine which will be useful in doing so. The first technique is iterative…
In this paper, we consider the network slicing problem which attempts to map multiple customized virtual network requests (also called services) to a common shared network infrastructure and allocate network resources to meet diverse…
In this paper we propose a new approach for developing a proof that P=NP. We propose to use a polynomial-time reduction of a NP-complete problem to Linear Programming. Earlier such attempts used polynomial-time transformation which is a…
Polygons are a paramount data structure in computational geometry. While the complexity of many algorithms on simple polygons or polygons with holes depends on the size of the input polygon, the intrinsic complexity of the problems these…
Matrices with low numerical rank are omnipresent in many signal processing and data analysis applications. The pivoted QLP (p-QLP) algorithm constructs a highly accurate approximation to an input low-rank matrix. However, it is…
In this paper, an exact algorithm in polynomial time is developed to solve unrestricted binary quadratic programs. The computational complexity is $O\left( n^{\frac{15}{2}}\right) $, although very conservative, it is sufficient to prove…
In this paper, we provide the first provable linear-time (in the number of non-zero entries of the input) algorithm for approximately solving the generalized trust region subproblem (GTRS) of minimizing a quadratic function over a quadratic…
Joint object matching, also known as multi-image matching, namely, the problem of finding consistent partial maps among all pairs of objects within a collection, is a crucial task in many areas of computer vision. This problem subsumes…
Positive linear programs (LP), also known as packing and covering linear programs, are an important class of problems that bridges computer science, operations research, and optimization. Despite the consistent efforts on this problem, all…
Computation of (approximate) polynomials common factors is an important problem in several fields of science, like control theory and signal processing. While the problem has been widely studied for scalar polynomials, the scientific…