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We study the problem of finding solutions to the stable matching problem that are robust to errors in the input and we obtain a polynomial time algorithm for a special class of errors. In the process, we also initiate work on a new…
The large sparse linear systems arising from the finite element or finite difference discretization of elliptic PDEs can be solved directly via, e.g., nested dissection or multifrontal methods. Such techniques reorder the nodes in the grid…
Time series data arising in many applications nowadays are high-dimensional. A large number of parameters describe features of these time series. We propose a novel approach to modeling a high-dimensional time series through several…
Understanding the singular value spectrum of a matrix $A \in \mathbb{R}^{n \times n}$ is a fundamental task in countless applications. In matrix multiplication time, it is possible to perform a full SVD and directly compute the singular…
Semidefinite programs (SDPs) are a fundamental class of optimization problems with important recent applications in approximation algorithms, quantum complexity, robust learning, algorithmic rounding, and adversarial deep learning. This…
Exactly computing the full output distribution of linear optical circuits remains a challenge, as existing methods are either time-efficient but memory-intensive or memory-efficient but slow. Moreover, any realistic simulation must account…
In this paper we present a new algorithm for solving linear programs that requires only $\tilde{O}(\sqrt{rank(A)}L)$ iterations to solve a linear program with $m$ constraints, $n$ variables, and constraint matrix $A$, and bit complexity…
An iterative algorithm is presented for solving the RPA equations of linear response. The method optimally computes the energy-weighted moments of the strength function, allowing one to match the computational effort to the intrinsic…
This paper studies optimal matroid partitioning problems for various objective functions. In the problem, we are given a finite set $E$ and $k$ weighted matroids $(E, \mathcal{I}_i, w_i)$, $i = 1, \dots, k$, and our task is to find a…
We present a novel algorithm attaining excessively fast, the sought solution of linear systems of equations. The algorithm is short in its basic formulation and, by definition, vectorized, while the memory allocation demands are trivial,…
In this paper we present the first deterministic polynomial time algorithm for determining the existence of a Hamiltonian cycle and finding a Hamiltonian cycle in general graphs. Our algorithm can also solve the Hamiltonian path problem in…
In this article we describe an algorithm that can be applied for the generation of various classes of maps on orientable surfaces. It uses existing generators for abstract graphs and combines them with an efficient embedding and isomorphism…
This note provides new methods for constructing quadratic nonresidues in finite fields of characteristic p. It will be shown that there is an effective deterministic polynomial time algorithm for constructing quadratic nonresidues in finite…
We introduce a new width parameter for matroids called decomposition width and prove that every matroid property expressible in the monadic second order logic can be computed in linear time for matroids with bounded decomposition width if…
Recently increasing penetration of renewable energy generation brings challenges for power system operators to perform efficient power generation daily scheduling, due to the intermittent nature of the renewable generation and discrete…
Linear rank-width is a linearized variation of rank-width, and it is deeply related to matroid path-width. In this paper, we show that the linear rank-width of every $n$-vertex distance-hereditary graph, equivalently a graph of rank-width…
Given a non-empty genus in $n$ dimensions with determinant $d$, we give a randomized algorithm that outputs a quadratic form from this genus. The time complexity of the algorithm is poly$(n,\log d)$; assuming Generalized Riemann Hypothesis…
In this paper we consider the classic matroid intersection problem: given two matroids $\M_{1}=(V,\I_{1})$ and $\M_{2}=(V,\I_{2})$ defined over a common ground set $V$, compute a set $S\in\I_{1}\cap\I_{2}$ of largest possible cardinality,…
We present an algorithm computing the determinant of an integer matrix A. The algorithm is introspective in the sense that it uses several distinct algorithms that run in a concurrent manner. During the course of the algorithm partial…
Zonotopes are becoming an increasingly popular set representation for formal verification techniques. This is mainly due to their efficient representation and their favorable computational complexity of important operations in…