Related papers: Faster algorithms on linear delta-matroids
Matroids, particularly linear ones, have been a powerful tool in parameterized complexity for algorithms and kernelization. They have sped up or replaced dynamic programming. Delta-matroids generalize matroids by encapsulating structures…
Determinant maximization problem gives a general framework that models problems arising in as diverse fields as statistics \cite{pukelsheim2006optimal}, convex geometry \cite{Khachiyan1996}, fair allocations\linebreak \cite{anari2016nash},…
We initiate the study of matroid problems in a new oracle model called dynamic oracle. Our algorithms in this model lead to new bounds for some classic problems, and a "unified" algorithm whose performance matches previous results developed…
We consider a fast approximation algorithm for the linear matroid intersection problem. In this problem, we are given two $r \times n$ matrices $M_1$ and $M_2$, and the objective is to find a largest set of columns that are linearly…
Determinant maximization provides an elegant generalization of problems in many areas, including convex geometry, statistics, machine learning, fair allocation of goods, and network design. In an instance of the determinant maximization…
Matrix representations are a powerful tool for designing efficient algorithms for combinatorial optimization problems such as matching, and linear matroid intersection and parity. In this paper, we initiate the study of matrix…
The maximum common subtree isomorphism problem asks for the largest possible isomorphism between subtrees of two given input trees. This problem is a natural restriction of the maximum common subgraph problem, which is ${\sf NP}$-hard in…
Recent results by Harrow et. al. and by Ta-Shma, suggest that quantum computers may have an exponential advantage in solving a wealth of linear algebraic problems, over classical algorithms. Building on the quantum intuition of these…
We present a polynomial time algorithm to approximately scale tensors of any format to arbitrary prescribed marginals (whenever possible). This unifies and generalizes a sequence of past works on matrix, operator and tensor scaling. Our…
The matroid parity (or matroid matching) problem, introduced as a common generalization of matching and matroid intersection problems, is so general that it requires an exponential number of oracle calls. Nevertheless, Lov\'asz (1980)…
Basic path-matchings, introduced by Cunningham and Geelen (FOCS 1996), are a common generalization of matroid intersection and non-bipartite matching. The main results of this paper are a new algebraic characterization of basic…
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…
We describe approximation algorithms in Linial's classic LOCAL model of distributed computing to find maximum-weight matchings in a hypergraph of rank $r$. Our main result is a deterministic algorithm to generate a matching which is an…
For an $n$-element matroid $M$ given by an $n \times n$ matrix representation over a finite field $\mathbb F$ and an integer $k$, we present an $(O_{k,\mathbb F}(n^2)+O(n^\omega))$-time algorithm that either finds a branch-decomposition of…
In this paper, we address the weighted linear matroid intersection problem from the computation of the degree of the determinants of a symbolic matrix. We show that a generic algorithm computing the degree of noncommutative determinants,…
Fast matrix multiplication is one of the most fundamental problems in algorithm research. The exponent of the optimal time complexity of matrix multiplication is usually denoted by $\omega$. This paper discusses new ideas for improving the…
We investigate the complexity of several fundamental polynomial-time solvable problems on graphs and on matrices, when the given instance has low treewidth; in the case of matrices, we consider the treewidth of the graph formed by non-zero…
We consider fast algorithms for monotone submodular maximization subject to a matroid constraint. We assume that the matroid is given as input in an explicit form, and the goal is to obtain the best possible running times for important…
The fastest known algorithms for dealing with structured matrices, in the sense of the displacement rank measure, are randomized. For handling classical displacement structures, they achieve the complexity bounds…
Multi-task learning (MTL) has emerged as a pivotal paradigm in machine learning by leveraging shared structures across multiple related tasks. Despite its empirical success, the development of likelihood-based efficiently solvable…