arXiv subjects

Judit Nagy-György

Publications and source records attributed to Judit Nagy-György.

6 recordsLinked to original sources

arXiv2024

On the Advice Complexity of Online Matching on the Line

We consider the matching problem on the line with advice complexity. We give a 1-competitive online algorithm with advice complexity $n-1,$ and show that there is no 1-competitive online algorithm reading less than $n-1$ bits of advice. Moreover, for each $0<k<n$ we present a $c(n/k)$-competitive online algorithm with advice complexity $O(k(\log N + \log n))$ where $n$ is the number of servers, $N$ is the distance of the minimal and maximal servers, and $c(n)$ is the complexity of the best online algorithm without advice.

cs.DS↗

arXiv2024

On the Advice Complexity of Online Unit Clustering

In online unit clustering, points of a metric space arriving one by one must be partitioned into clusters of diameter at most 1, where the cost is the number of clusters. This paper gives linear upper and lower bounds on the advice complexity of 1-competitive online unit clustering algorithms, in terms of the number of points in $\mathbb{R}^d$ and $\mathbb{Z}^d$.

cs.DS↗

arXiv2023

Book free $3$-Uniform Hypergraphs

A $k$-book in a hypergraph consists of $k$ Berge triangles sharing a common edge. In this paper we prove that the number of the hyperedges in a $k$-book-free 3-uniform hypergraph on $n$ vertices is at most $\frac{n^2}{8}(1+o(1))$.

math.CO↗

arXiv2018

Embedding graphs having Ore-degree at most five

Let $H$ and $G$ be graphs on $n$ vertices, where $n$ is sufficiently large. We prove that if $H$ has Ore-degree at most 5 and $G$ has minimum degree at least $2n/3$ then $H\subset G.$

math.CO↗

arXiv2014

Biclique coverings, rectifier networks and the cost of $\varepsilon$-removal

We relate two complexity notions of bipartite graphs: the minimal weight biclique covering number $\mathrm{Cov}(G)$ and the minimal rectifier network size $\mathrm{Rect}(G)$ of a bipartite graph $G$. We show that there exist graphs with $\mathrm{Cov}(G)\geq \mathrm{Rect}(G)^{3/2-ε}$. As a corollary, we establish that there exist nondeterministic finite automata (NFAs) with $\varepsilon$-transitions, having $n$ transitions total such that the smallest equivalent $\varepsilon$-free NFA has $Ω(n^{3/2-ε})$ transitions. We also formulate a version of previous bounds for the weighted set cover problem and discuss its connections to giving upper bounds for the possible blow-up.

cs.FL↗

arXiv2007

Randomized algorithm for the k-server problem on decomposable spaces

We study the randomized k-server problem on metric spaces consisting of widely separated subspaces. We give a method which extends existing algorithms to larger spaces with the growth rate of the competitive quotients being at most O(log k). This method yields o(k)-competitive algorithms solving the randomized k-server problem, for some special underlying metric spaces, e.g. HSTs of "small" height (but unbounded degree). HSTs are important tools for probabilistic approximation of metric spaces.

cs.DS↗