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Online coloring graphs with high girth and high oddgirth [article]

Judit Nagy-Gyorgy
2009 arXiv   pre-print
We give an upper bound for the online chromatic number of graphs with high girth and for graphs with high oddgirth generalizing Kier- stead's algorithm for graphs that contain neither a C3 or C5 as an induced subgraph.
arXiv:0907.3420v1 fatcat:akc2blw5pfamzcywfqjfi63zy4

Biclique coverings, rectifier networks and the cost of ε-removal [article]

Szabolcs Iván, Ádám Dániel Lelkes, Judit Nagy-György, Balázs Szörényi, György Turán
2014 arXiv   pre-print
We relate two complexity notions of bipartite graphs: the minimal weight biclique covering number Cov(G) and the minimal rectifier network size Rect(G) of a bipartite graph G. We show that there exist graphs with Cov(G)≥Rect(G)^3/2-ϵ. As a corollary, we establish that there exist nondeterministic finite automata (NFAs) with ε-transitions, having n transitions total such that the smallest equivalent ε-free NFA has Ω(n^3/2-ϵ) transitions. We also formulate a version of previous bounds for the
more » ... hted set cover problem and discuss its connections to giving upper bounds for the possible blow-up.
arXiv:1406.0017v1 fatcat:ywaxx47yrbf4lgzkmr6fbb26yi

Randomized algorithm for the k-server problem on decomposable spaces [article]

Judit Nagy-György
2007 arXiv   pre-print
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.
arXiv:0708.2351v1 fatcat:dbrtrzsfffhvxh5qzlirzwvtoq

Book free 3-Uniform Hypergraphs [article]

Debarun Ghosh, Ervin Győri, Judit Nagy-György, Addisu Paulos, Chuanqi Xiao, Oscar Zamora
2021 arXiv   pre-print
Nagy-György research was partially supported by the National Research, Development, and Innovation Office, NKFIH grant KH 129597.  ... 
arXiv:2110.01184v1 fatcat:2wnugg6cqneyvhq6qndhfhnb6u

On the structure and syntactic complexity of generalized definite languages [article]

Szabolcs Ivan, Judit Nagy-Gyorgy
2013 arXiv   pre-print
We give a forbidden pattern characterization for the class of generalized definite languages, show that the corresponding problem is NL-complete and can be solved in quadratic time. We also show that their syntactic complexity coincides with that of the definite languages and give an upper bound of n! for this measure.
arXiv:1304.5714v1 fatcat:5xte65ln4zdixooj3iyv2rkgce

On nonpermutational transformation semigroups with an application to syntactic complexity [article]

Szabolcs Ivan, Judit Nagy-Gyorgy
2014 arXiv   pre-print
We give an upper bound of n((n-1)!-(n-3)!) for the possible largest size of a subsemigroup of the full transformational semigroup over n elements consisting only of nonpermutational transformations. As an application we gain the same upper bound for the syntactic complexity of (generalized) definite languages as well.
arXiv:1402.7289v1 fatcat:kb6jyj656zguzn5tl5clplmham

Online hypergraph coloring with rejection

Csanád Imreh, Judit Nagy-György
2015 Acta Universitatis Sapientiae: Informatica  
In this paper we investigate the online hypergraph coloring problem with rejection, where the algorithm is allowed to reject a vertex instead of coloring it but each vertex has a penalty which has to be paid if it is not colored. The goal is to minimize the sum of the number of the used colors for the accepted vertices and the total penalty paid for the rejected ones. We study the online problem which means that the algorithm receives the vertices of the hypergraph in some order v1, . . . , vn
more » ... nd it must decide about vi by only looking at the subhypergraph Hi = (Vi, Ei) where Vi = {v1, . . . , vi} and Ei contains the edges of the hypergraph which are subsets of Vi. We consider two models: in the full edge model only the edges where each vertex is accepted must be well-colored, in the trace model the subsets of the edges formed by the accepted vertices must be well colored as well. We consider proper and conflict free colorings. We present in each cases optimal online algorithms in the sense that they achieve asymptotically the smallest possible competitive ratio.
doi:10.1515/ausi-2015-0009 fatcat:y5dqfoxo5rapzkw6s5gi32gska

Online File Caching with Rejection Penalties

Leah Epstein, Csanád Imreh, Asaf Levin, Judit Nagy-György
2013 Algorithmica  
In the file caching problem, the input is a sequence of requests for files out of a slow memory. A file has two attributes, a positive retrieval cost and an integer size. An algorithm is required to maintain a cache of size k such that the total size of files stored in the cache never exceeds k. Given a request for a file that is not present in the cache at the time of request, the file must be brought from the slow memory into the cache, possibly evicting other files from the cache. This
more » ... a cost equal to the retrieval cost of the requested file. Well-known special cases include paging (all costs and sizes are equal to 1), the cost model, which is also known as weighted paging, (all sizes are equal to 1), the fault model (all costs are equal to 1), and the bit model (the cost of a file is equal to its size). If bypassing is allowed, a miss for a file still results in an access to this file in the slow memory, but its subsequent insertion into the cache is optional. We study a new online variant of caching, called caching with rejection. In this variant, each request for a file has a rejection penalty associated with the request. The penalty of a request is given to the algorithm together with the request. When a file that is not present in the cache is requested, the algorithm must either bring the file into the cache, paying the retrieval cost of the file, or reject the file, paying the rejection penalty of the request. The objective function is the sum of total rejection penalty and the total retrieval cost. This problem generalizes both caching and caching with bypassing. We design deterministic and randomized algorithms for this problem. The competitive ratio of the randomized algorithm is O(log k), and this is optimal up to a constant factor. In the deterministic case, a k-competitive algorithm for caching, and a (k + 1)-competitive algorithm for caching with bypassing are known. Moreover, these are the best possible competitive ratios. In contrast, we present a lower bound of 2k + 1 on the competitive ratio of any deterministic algorithm for the variant with rejection. The lower bound is valid already for paging. We design a (2k + 2)-competitive algorithm for caching with rejection. We also design a different (2k + 1)-competitive algorithm, that can be used for paging and for caching in the bit and fault models.
doi:10.1007/s00453-013-9793-0 fatcat:zm7na3bmgvamdnylhgzmhzchxu

SCHIZOBANK – The Hungarian national schizophrenia biobank and its role in schizophrenia research

Gabriella Inczédy-Farkas, Judit Benkovits, Nóra Balogh, Péter Álmos, Beáta Scholtz, Gábor Zahuczky, Zsolt Török, Krisztián Nagy, János Réthelyi, Zoltán Makkos, Ákos Kassai-Farkas, Anikó Égerházy (+6 others)
2010 Orvosi Hetilap  
A multifaktoriális betegségek patogenezisének vizsgálata a posztgenomiális éra nagy kihívása.  ...  Közleményünkben egy olyan konzorciális biobankról (SCHIZOBANK) számolunk be, amelynek építését a hazai akadémiai szféra és gyógyszeripar kezdeményezésére a Schizo-08 Konzorcium vezetése mellett öt nagy  ...  A multifaktoriális betegségek patogenezisének vizsgálata a posztgenomiális éra nagy kihívása.  ... 
doi:10.1556/oh.2010.28943 pmid:20719713 fatcat:7srlwl5f25bnjp5245eysitfcy

Biclique Coverings, Rectifier Networks and the Cost of ε-Removal [chapter]

Szabolcs Iván, Ádám D. Lelkes, Judit Nagy-György, Balázs Szörényi, György Turán
2014 Lecture Notes in Computer Science  
We relate two complexity notions of bipartite graphs: the minimal weight biclique covering number Cov(G) and the minimal rectifier network size Rect(G) of a bipartite graph G. We show that there exist graphs with Cov(G) ≥ Rect(G) 3/2−ǫ . As a corollary, we establish that there exist nondeterministic finite automata (NFAs) with εtransitions, having n transitions total such that the smallest equivalent ε-free NFA has Ω(n 3/2−ǫ ) transitions. We also formulate a version of previous bounds for the
more » ... eighted set cover problem and discuss its connections to giving upper bounds for the possible blow-up. ⋆
doi:10.1007/978-3-319-09704-6_16 fatcat:ryftga3625ffxdc3mlpw7yw3su

Embedding graphs having Ore-degree at most five [article]

Béla Csaba, Judit Nagy-György
2018 arXiv   pre-print
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⊂ G.
arXiv:1707.07216v2 fatcat:oxzoi6kc7nbkvfl5jluwab657a

On Nonpermutational Transformation Semigroups with an Application to Syntactic Complexity

Szabolcs Iván, Judit Nagy-György
2016 Acta Cybernetica  
We give an upper bound of n((n−1)!−(n−3)!) for the possible largest size of a subsemigroup of the full transformational semigroup over n elements consisting only of nonpermutational transformations. As an application we gain the same upper bound for the syntactic complexity of (generalized) definite languages as well.
doi:10.14232/actacyb.22.3.2016.9 fatcat:xrfbkivuuzgqjan7miaelavjn4

Embedding Graphs Having Ore-Degree at Most Five

Béla Csaba, Judit Nagy-György
2019 SIAM Journal on Discrete Mathematics  
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 is a subgraph of G.
doi:10.1137/17m1155442 fatcat:wahtxixkfvbgze75fdrschm224

Randomized algorithm for the k-server problem on decomposable spaces

Judit Nagy-György
2009 Journal of Discrete Algorithms  
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.
doi:10.1016/j.jda.2009.02.005 fatcat:d3267f4pcnd4le5rgtlt54cjlu

On the Advice Complexity of Coloring Bipartite Graphs and Two-Colorable Hypergraphs

Judit Nagy-György
2018 Acta Cybernetica  
In the online coloring problem the vertices are revealed one by one to an online algorithm, which has to color them immediately as they appear. The advice complexity attempts to measure how much knowledge of the future is neccessary to achieve a given competitive ratio. Here, we examine coloring of bipartite graphs, proper and the conflict-free coloring of k-uniform hypergraphs and we provide lower and upper bounds for the number of bits of advice to achieve the optimal cost. For bipartite
more » ... s the upper bound n − 2 is tight. For the proper coloring, n − 2k bits are necessary and n − 2 bits are sufficient, while for the conflict-free coloring case n − 2 bits of advice are neccessary and sufficient to color optimally if k > 3.
doi:10.14232/actacyb.23.3.2018.13 fatcat:rtdro2gdgvgbfpaysu25wqhhvi
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