Related papers: A Bad Example for Jain's Iterative Rounding Theore…
Given a set $P$ of $n$ points in the plane, {\sc Covering Points by Lines} is the problem of finding a minimum-cardinality set $\L$ of lines such that every point $p \in P$ is incident to some line $\ell \in \L$. As a geometric variant of…
Motivated by the study of matrix elimination orderings in combinatorial scientific computing, we utilize graph sketching and local sampling to give a data structure that provides access to approximate fill degrees of a matrix undergoing…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
Johnson and Lindenstrauss (Contemporary Mathematics, 1984) showed that for $n > m$, a scaled random projection $\mathbf{A}$ from $\mathbb{R}^n$ to $\mathbb{R}^m$ is an approximate isometry on any set $S$ of size at most exponential in $m$.…
Typical behavior of the linear programming problem (LP) is studied as a relaxation of the minimum vertex cover problem, which is a type of the integer programming problem (IP). To deal with the LP and IP by statistical mechanics, a…
A classical result in undirected wireline networks is the near optimality of routing (flow) for multiple-unicast traffic (multiple sources communicating independent messages to multiple destinations): the min cut upper bound is within a…
The growing amount of applications that generate vast amount of data in short time scales render the problem of partial monitoring, coupled with prediction, a rather fundamental one. We study the aforementioned canonical problem under the…
We revisit the minimum-link path problem: Given a polyhedral domain and two points in it, connect the points by a polygonal path with minimum number of edges. We consider settings where the vertices and/or the edges of the path are…
We consider the following general scheduling problem: The input consists of n jobs, each with an arbitrary release time, size, and a monotone function specifying the cost incurred when the job is completed at a particular time. The…
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…
We show that several problems of compacting orthogonal graph drawings to use the minimum number of rows, area, length of longest edge or total edge length cannot be approximated better than within a polynomial factor of optimal in…
The matrix completion problem consists of finding or approximating a low-rank matrix based on a few samples of this matrix. We propose a new algorithm for matrix completion that minimizes the least-square distance on the sampling set over…
Combinatorial optimization is among the main applications envisioned for near-term and fault-tolerant quantum computers. In this work, we consider a well-studied quantum algorithm for combinatorial optimization: the Quantum Approximate…
In this paper, we take a unified approach for network information theory and prove a coding theorem, which can recover most of the achievability results in network information theory that are based on random coding. The final single-letter…
This article presents a compact implementation of a recently proposed strongly polynomial-time algorithm for the general linear programming problem. Each iteration of the algorithm consists of applying a pair of complementary Gauss-Jordan…
Iterative refinement is particularly popular for numerical solution of linear systems of equations. We extend it to Low Rank Approximation of a matrix (LRA) and observe close link of the resulting algorithm to oversampling techniques,…
Clustering bipartite graphs is a fundamental task in network analysis. In the high-dimensional regime where the number of rows $n_1$ and the number of columns $n_2$ of the associated adjacency matrix are of different order, existing methods…
We propose a successive generation of cutting inequalities for binary quadratic optimization problems. Multiple cutting inequalities are successively generated for the convex hull of the set of the optimal solutions $\subset \{0, 1\}^n$,…
Many classical and modern machine learning algorithms require solving optimization tasks under orthogonality constraints. Solving these tasks with feasible methods requires a gradient descent update followed by a retraction operation on the…
We focus on designing combinatorial algorithms for the Capacitated Network Design problem (Cap-SNDP). The Cap-SNDP is the problem of satisfying connectivity requirements when edges have costs and hard capacities. We begin by showing that…