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

2009
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arXiv
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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
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Biclique coverings, rectifier networks and the cost of ε-removal
[article]

2014
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arXiv
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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

arXiv:1406.0017v1
fatcat:ywaxx47yrbf4lgzkmr6fbb26yi
## more »

... hted set cover problem and discuss its connections to giving upper bounds for the possible blow-up.##
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Randomized algorithm for the k-server problem on decomposable spaces
[article]

2007
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arXiv
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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
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Book free 3-Uniform Hypergraphs
[article]

2021
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arXiv
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pre-print

*Nagy*-

*György*research was partially supported by the National Research, Development, and Innovation Office, NKFIH grant KH 129597. ...

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

2013
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arXiv
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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
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On nonpermutational transformation semigroups with an application to syntactic complexity
[article]

2014
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arXiv
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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
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Online hypergraph coloring with rejection

2015
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Acta Universitatis Sapientiae: Informatica
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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

doi:10.1515/ausi-2015-0009
fatcat:y5dqfoxo5rapzkw6s5gi32gska
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... 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.##
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Online File Caching with Rejection Penalties

2013
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Algorithmica
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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

doi:10.1007/s00453-013-9793-0
fatcat:zm7na3bmgvamdnylhgzmhzchxu
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... 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.##
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SCHIZOBANK – The Hungarian national schizophrenia biobank and its role in schizophrenia research

2010
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Orvosi Hetilap
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A multifaktoriális betegségek patogenezisének vizsgálata a posztgenomiális éra

doi:10.1556/oh.2010.28943
pmid:20719713
fatcat:7srlwl5f25bnjp5245eysitfcy
*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. ...##
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Biclique Coverings, Rectifier Networks and the Cost of ε-Removal
[chapter]

2014
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Lecture Notes in Computer Science
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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

doi:10.1007/978-3-319-09704-6_16
fatcat:ryftga3625ffxdc3mlpw7yw3su
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... eighted set cover problem and discuss its connections to giving upper bounds for the possible blow-up. ⋆##
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Embedding graphs having Ore-degree at most five
[article]

2018
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arXiv
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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
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On Nonpermutational Transformation Semigroups with an Application to Syntactic Complexity

2016
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Acta Cybernetica
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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
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Embedding Graphs Having Ore-Degree at Most Five

2019
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SIAM Journal on Discrete Mathematics
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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
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Randomized algorithm for the k-server problem on decomposable spaces

2009
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Journal of Discrete Algorithms
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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
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On the Advice Complexity of Coloring Bipartite Graphs and Two-Colorable Hypergraphs

2018
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Acta Cybernetica
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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

doi:10.14232/actacyb.23.3.2018.13
fatcat:rtdro2gdgvgbfpaysu25wqhhvi
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... 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.
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