Related papers: Dynamic Matroids: Base Packing and Covering
We provide a framework for the design and analysis of dynamic programming algorithms for surface-embedded graphs on n vertices and branchwidth at most k. Our technique applies to general families of problems where standard dynamic…
We study the parallel complexity of finding a basis of a graphic matroid under independence-oracle access. Karp, Upfal, and Wigderson (FOCS 1985, JCSS 1988) initiated the study of this problem and established two algorithms for finding a…
Embedding static graphs in low-dimensional vector spaces plays a key role in network analytics and inference, supporting applications like node classification, link prediction, and graph visualization. However, many real-world networks…
We study the complexity of testing if two given matroids are isomorphic. The problem is easily seen to be in $\Sigma_2^p$. In the case of linear matroids, which are represented over polynomially growing fields, we note that the problem is…
We prove that for every proper minor-closed class $M$ of matroids representable over a prime field, there exists a constant-competitive matroid secretary algorithm for the matroids in $M$. This result relies on the extremely powerful…
We present deterministic algorithms for maintaining a $(3/2 + \epsilon)$ and $(2 + \epsilon)$-approximate maximum matching in a fully dynamic graph with worst-case update times $\hat{O}(\sqrt{n})$ and $\tilde{O}(1)$ respectively. The…
We give the first non-trivial fully dynamic probabilistic tree embedding algorithm for weighted graphs undergoing edge insertions and deletions. We obtain a trade-off between amortized update time and expected stretch against an oblivious…
Consider a distributed task where the communication network is fixed but the local inputs given to the nodes of the distributed system may change over time. In this work, we explore the following question: if some of the local inputs…
In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…
In mathematics and computer science, connectivity is one of the basic concepts of matroid theory: it asks for the minimum number of elements which need to be removed to disconnect the remaining nodes from each other. It is closely related…
The main result is Theorem MAT 11 which states that every finite closure operator is the ground set of a matroid. Its base sets consist of nonredundant covers of of the closure. These are minimal subsets that determine the closure operator…
The secretary problem became one of the most prominent online selection problems due to its numerous applications in online mechanism design. The task is to select a maximum weight subset of elements subject to given constraints, where…
In the recent years, several polynomial algorithms of a dynamical nature have been proposed to address the graph isomorphism problem. In this paper we propose a generalization of an approach exposed in cond-mat/0209112 and find that this…
Pose graph optimization is a special case of the simultaneous localization and mapping problem where the only variables to be estimated are pose variables and the only measurements are inter-pose constraints. The vast majority of pose graph…
We study determinantal varieties from conditional independence models with hidden variables, focusing on their irreducible decompositions, dimensions, degrees, and Gr\"obner bases. Each variety encodes a collection of matroids, whose flats…
In the Matroid Secretary Problem, introduced by Babaioff et al. [SODA 2007], the elements of a given matroid are presented to an online algorithm in random order. When an element is revealed, the algorithm learns its weight and decides…
The way circuits, relative to a basis, are affected as a result of exchanging a basis element, is studied. As consequences, it is shown that three consecutive symmetric exchanges exist for any two bases of a matroid, and that a full serial…
We consider the PageRank problem in the dynamic setting, where the goal is to explicitly maintain an approximate PageRank vector $\pi \in \mathbb{R}^n$ for a graph under a sequence of edge insertions and deletions. Our main result is a…
We show new algorithms and constructions over linear delta-matroids. We observe an alternative representation for linear delta-matroids, as a contraction representation over a skew-symmetric matrix. This is equivalent to the more standard…
We consider the problem of maintaining a maximal independent set (MIS) in a dynamic graph subject to edge insertions and deletions. Recently, Assadi, Onak, Schieber and Solomon (STOC 2018) showed that an MIS can be maintained in sublinear…