English
Related papers

Related papers: Online Disjoint Set Covers: Randomization is not N…

200 papers

We resolve the fundamental problem of online decoding with general $n^{th}$ order ergodic Markov chain models. Specifically, we provide deterministic and randomized algorithms whose performance is close to that of the optimal offline…

Machine Learning · Computer Science 2019-05-31 Vikas K. Garg , Tamar Pichkhadze

We study the discrete bin covering problem where a multiset of items from a fixed set $S \subseteq (0,1]$ must be split into disjoint subsets while maximizing the number of subsets whose contents sum to at least $1$. We study the online…

Data Structures and Algorithms · Computer Science 2024-01-29 Magnus Berg , Shahin Kamali

Recent breakthroughs in graph streaming have led to the design of single-pass semi-streaming algorithms for various graph coloring problems such as $(\Delta+1)$-coloring, degeneracy-coloring, coloring triangle-free graphs, and others. These…

Data Structures and Algorithms · Computer Science 2021-10-01 Sepehr Assadi , Andrew Chen , Glenn Sun

In recent years, there has been a growing interest in solving various graph coloring problems in the streaming model. The initial algorithms in this line of work are all crucially randomized, raising natural questions about how important a…

Data Structures and Algorithms · Computer Science 2022-12-22 Sepehr Assadi , Amit Chakrabarti , Prantar Ghosh , Manuel Stoeckl

This paper improves and in two cases nearly settles, up to logarithmically lower-order factors, the deterministic complexity of some of the most central problems in distributed graph algorithms, which have been studied for over three…

Data Structures and Algorithms · Computer Science 2024-10-28 Mohsen Ghaffari , Christoph Grunau

Consider the following random process: The vertices of a binomial random graph $G_{n,p}$ are revealed one by one, and at each step only the edges induced by the already revealed vertices are visible. Our goal is to assign to each vertex one…

Combinatorics · Mathematics 2018-02-16 Torsten Mütze , Thomas Rast , Reto Spöhel

We consider the online version of the piercing set problem, where geometric objects arrive one by one, and the online algorithm must maintain a valid piercing set for the already arrived objects by making irrevocable decisions. It is easy…

Computational Geometry · Computer Science 2024-07-04 Minati De , Saksham Jain , Sarat Varma Kallepalli , Satyam Singh

In this paper, we study the problem of computing an edge-coloring in the (one-pass) W-streaming model. In this setting, the edges of an $n$-node graph arrive in an arbitrary order to a machine with a relatively small space, and the goal is…

Data Structures and Algorithms · Computer Science 2024-04-18 Shiri Chechik , Doron Mukhtar , Tianyi Zhang

A colouring of a hypergraph's vertices is polychromatic if every hyperedge contains at least one vertex of each colour; the polychromatic number is the maximum number of colours in such a colouring. Its dual, the cover-decomposition number,…

Combinatorics · Mathematics 2012-05-31 Béla Bollobás , David Pritchard , Thomas Rothvoß , Alex Scott

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…

Data Structures and Algorithms · Computer Science 2023-10-13 David G. Harris

In the Connected Vertex Cover problem we are given an undirected graph G together with an integer k and we are to find a subset of vertices X of size at most k, such that X contains at least one end-point of each edge and moreover X induces…

Data Structures and Algorithms · Computer Science 2012-03-01 Marek Cygan

Network decomposition is a central tool in distributed graph algorithms. We present two improvements on the state of the art for network decomposition, which thus lead to improvements in the (deterministic and randomized) complexity of…

Data Structures and Algorithms · Computer Science 2020-07-17 Mohsen Ghaffari , Christoph Grunau , Václav Rozhoň

Several algorithms with an approximation guarantee of $O(\log n)$ are known for the Set Cover problem, where $n$ is the number of elements. We study a generalization of the Set Cover problem, called the Partition Set Cover problem. Here,…

Data Structures and Algorithms · Computer Science 2018-12-04 Tanmay Inamdar , Kasturi Varadarajan

We consider fractional online covering problems with $\ell_q$-norm objectives. The problem of interest is of the form $\min\{ f(x) \,:\, Ax\ge 1, x\ge 0\}$ where $f(x)=\sum_{e} c_e \|x(S_e)\|_{q_e} $ is the weighted sum of $\ell_q$-norms…

Data Structures and Algorithms · Computer Science 2017-05-10 Viswanath Nagarajan , Xiangkun Shen

Locally finding a solution to symmetry-breaking tasks such as vertex-coloring, edge-coloring, maximal matching, maximal independent set, etc., is a long-standing challenge in distributed network computing. More recently, it has also become…

Data Structures and Algorithms · Computer Science 2017-02-03 Pierre Fraigniaud , Marc Heinrich , Adrian Kosowski

We study a family of closely-related distributed graph problems, which we call degree splitting, where roughly speaking the objective is to partition (or orient) the edges such that each node's degree is split almost uniformly. Our findings…

Data Structures and Algorithms · Computer Science 2016-08-11 Mohsen Ghaffari , Hsin-Hao Su

Consider the following online version of the submodular maximization problem under a matroid constraint: We are given a set of elements over which a matroid is defined. The goal is to incrementally choose a subset that remains independent…

Data Structures and Algorithms · Computer Science 2012-05-08 Niv Buchbinder , Joseph , Naor , R. Ravi , Mohit Singh

The classic theorem of Vizing (Diskret. Analiz.'64) asserts that any graph of maximum degree $\Delta$ can be edge colored (offline) using no more than $\Delta+1$ colors (with $\Delta$ being a trivial lower bound). In the online setting,…

Data Structures and Algorithms · Computer Science 2024-02-29 Joakim Blikstad , Ola Svensson , Radu Vintan , David Wajc

$ \renewcommand{\tilde}{\widetilde} $We present an $\tilde{O}(\log^2 n)$ round deterministic distributed algorithm for the maximal independent set problem. By known reductions, this round complexity extends also to maximal matching,…

Data Structures and Algorithms · Computer Science 2023-03-29 Mohsen Ghaffari , Christoph Grunau

We provide the first online algorithm for spectral hypergraph sparsification. In the online setting, hyperedges with positive weights are arriving in a stream, and upon the arrival of each hyperedge, we must irrevocably decide whether or…

Data Structures and Algorithms · Computer Science 2023-11-08 Tasuku Soma , Kam Chuen Tung , Yuichi Yoshida