Filters








1,408 Hits in 2.1 sec

Online hypergraph coloring

J. Nagy-György, Cs. Imreh
2008 Information Processing Letters  
In this paper we investigate the online hypergraph coloring problem.  ...  We show that there exists no online hypergraph coloring algorithm with sublinear competitive ratio.  ...  Let A be an arbitrary online hypergraph coloring algorithm, define the online hypergraph H n,A on n vertices as follows.  ... 
doi:10.1016/j.ipl.2008.08.009 fatcat:3jkuv4p3f5dbhcboy25ig4xjmu

Online coloring of hypergraphs

Magnús M. Halldórsson
2010 Information Processing Letters  
We give a tight bound on randomized online coloring of hypergraphs. The bound holds even if the algorithm knows the hypergraph in advance (but not the ordering in which it is presented).  ...  More specifically, we show that for any n and k, there is a 2colorable k-uniform hypergraph on n vertices for which any randomized online coloring uses Ω(n/k) colors in expectation.  ...  Online Hypergraph Coloring A hypergraph H = (V, E) is formed by a set V of vertices and a collection E of subsets of V .  ... 
doi:10.1016/j.ipl.2010.03.001 fatcat:57jzbhifnjg5pcnzkuec4fcc7q

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  ...  We study the online problem which means that the algorithm receives the vertices of the hypergraph in some order v1, . . . , vn and it must decide about vi by only looking at the subhypergraph Hi = (Vi  ...  Online proper coloring of hypergarphs first was studied in [9] where it was proven that no online algorithm exists for 2-colorable k-uniform hypergraphs which can color them with less colors than n/(  ... 
doi:10.1515/ausi-2015-0009 fatcat:y5dqfoxo5rapzkw6s5gi32gska

Online Conflict-Free Colorings for Hypergraphs [chapter]

Amotz Bar-Noy, Panagiotis Cheilaris, Svetlana Olonetsky, Shakhar Smorodinsky
Lecture Notes in Computer Science  
i) We provide a framework for online conflict-free coloring (CF-coloring) any hypergraph.  ...  This is the first general efficient online CF-coloring for arbitrary kdegenerate hypergraphs.  ...  [6] initiated the study of online CF-coloring of hypergraphs.  ... 
doi:10.1007/978-3-540-73420-8_21 fatcat:plpgzy2lyngmfeio2bkg2faxgi

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.  ...  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  ...  FF uses the smallest color for each vertex which does not violate the rule of the coloring. The online graph was first defined in [12] , while the online hypergraph was first defined in [1] .  ... 
doi:10.14232/actacyb.23.3.2018.13 fatcat:rtdro2gdgvgbfpaysu25wqhhvi

Strong Colorings of Hypergraphs [chapter]

Geir Agnarsson, Magnús M. Halldórsson
2005 Lecture Notes in Computer Science  
We present nearly tight upper and lower bound on approximating general hypergraphs, both offline and online.  ...  A strong vertex coloring of a hypergraph assigns distinct colors to vertices that are contained in a common hyperedge. This captures many previously studied graph coloring problems.  ...  We consider both online and offline coloring algorithms.  ... 
doi:10.1007/978-3-540-31833-0_21 fatcat:wpgt4mjnfbaldfxx26dyyssyoe

Hitting Sets Online and Unique-Max Coloring [article]

Guy Even, Shakhar Smorodinsky
2012 arXiv   pre-print
The hypergraph (i.e., range-space consisting of points and ranges) is known in advance, and the ranges to be stabbed are input one-by-one in an online fashion.  ...  We consider hypergraphs in which the union of two intersecting ranges is also a range. Our main result for such hypergraphs is as follows.  ...  It equals the best competitive ratio achievable by any online deterministic algorithm with respect to the hypergraph H. I-type hypergraphs.  ... 
arXiv:1207.2598v1 fatcat:zh6y5og4ejbv5es5pgbvpvruei

Conflict-Free Coloring and its Applications [article]

Shakhar Smorodinsky
2012 arXiv   pre-print
Let H=(V,E) be a hypergraph. A conflict-free coloring of H is an assignment of colors to V such that in each hyperedge e ∈ E there is at least one uniquely-colored vertex.  ...  This notion is an extension of the classical graph coloring.  ...  [17] introduced an online version of the CF coloring problem.  ... 
arXiv:1005.3616v3 fatcat:mhap6v2hsjcvdh7s424vxgi5jm

Toric algebra of hypergraphs

Sonja Petrović, Despina Stasi
2013 Journal of Algebraic Combinatorics  
by the hypergraph.  ...  The edges of any hypergraph parametrize a monomial algebra called the edge subring of the hypergraph.  ...  Acknowledgements The authors thank György Turán for inspiring discussions, at the start of this project, about the fundamental problem of walks in hypergraphs; and also Elizabeth Gross for suggesting the  ... 
doi:10.1007/s10801-013-0444-y fatcat:jd63bo7j55aelezckllmxpqn3e

Online Disjoint Set Cover Without Prior Knowledge

Yuval Emek, Adam Goldbraikh, Erez Kantor, Michael Wagner
2019 European Symposium on Algorithms  
The disjoint set cover (DSC) problem is a fundamental combinatorial optimization problem concerned with partitioning the (hyper)edges of a hypergraph into (pairwise disjoint) clusters so that the number  ...  This paper investigates the competitiveness of online DSC algorithms.  ...  Let Alg(G) be the number of covering colors obtained by (online or offline) DSC algorithm Alg when invoked on hypergraph G.  ... 
doi:10.4230/lipics.esa.2019.44 dblp:conf/esa/EmekGK19 fatcat:6kkdwvebpbgqhpmjh3rqcdhpvm

Conflict-Free Coloring and its Applications [chapter]

Shakhar Smorodinsky
2013 Bolyai Society Mathematical Studies  
Let H = (V, E) be a hypergraph. A conflict-free coloring of H is an assignment of colors to V such that, in each hyperedge e ∈ E, there is at least one uniquely-colored vertex.  ...  We refer to such hypergraphs as hypergraphs induced by points on the line with respect to intervals or as the discrete intervals hypergraph. Trivially, we have χ(H) = 2.  ...  Degenerate hypergraphs Next, we describe the general framework of [10] for online CF-coloring any hypergraph.  ... 
doi:10.1007/978-3-642-41498-5_12 fatcat:gjf6tvt5yvgn3hlhuc3fcj3rda

An Optimal Algorithm for Conflict-Free Coloring for Tree of Rings [article]

Einollah Pira
2012 arXiv   pre-print
The coloring earned by this algorithm has the unique-min property, that is, the unique color is also minimum.  ...  A presented algorithm in [1] for a Tree of rings used O(log|T|.log|R|) colors but this algorithm uses O(log|T|+log|R|) colors.  ...  In [5] there is the online version of conflict-free coloring of a hypergraph. The online version of Connected Subgraphs Conflict-Free Coloring in chains was presented in [8] .  ... 
arXiv:1203.2414v1 fatcat:wsfhx4rcvrhqlhcdt2ogtu7id4

Strong-weak coupling duality between two perturbed quantum many-body systems: Calderbank-Shor-Steane codes and Ising-like systems

Mohammad Hossein Zarei
2017 Physical review B  
We show that the Hamiltonian corresponding to a CSS code on a hypergraph H which is perturbed by a uniform magnetic field is mapped to Hamiltonian of a Ising-like system on dual hypergraph H̃ in a transverse  ...  Graphs and recently hypergraphs have been known as an important tool for considering different properties of quantum many-body systems.  ...  FIG. 5 : 5 (Color online) Two sample lattice where a color code can be defined.  ... 
doi:10.1103/physrevb.96.165146 fatcat:mnrdjbmvkvhxlnf35dwwzln4ie

An Optimal Algorithm for Conflict-Free Coloring for Tree of Rings

Einollah Pira
2012 Computer Science & Engineering An International Journal  
The coloring earned by this algorithm has the unique-min property, that is, the unique color is also minimum.  ...  A presented algorithm in [1] for a Tree of rings used O(log|T|.log|R|) colors but this algorithm uses O(log|T|+log|R|) colors.  ...  In [5] there is the online version of conflict-free coloring of a hypergraph. The online version of Connected Subgraphs Conflict-Free Coloring in chains was presented in [8] .  ... 
doi:10.5121/cseij.2012.2101 fatcat:g66n3ftkunfhtfxde5asul5e2u

Deterministic conflict-free coloring for intervals

Amotz Bar-Noy, Panagiotis Cheilaris, Shakhar Smorodinsky
2008 ACM Transactions on Algorithms  
The problem can be modeled as a special vertex coloring problem for hypergraphs: In every hyperedge there must exist a vertex with a color that occurs exactly once in the hyperedge (the conflict-free property  ...  To the best of our knowledge, this is the first deterministic online algorithm using O(log n) colors, in a non-trivial online model.  ...  We introduce a hierarchy of four models for the above conflictfree coloring problem for hypergraphs: (i) static, (ii) dynamic offline, (iii) dynamic online with absolute positions, and (iv) dynamic online  ... 
doi:10.1145/1383369.1383375 fatcat:d4z5mhfzfrh6fgrkmwjmlh35ze
« Previous Showing results 1 — 15 out of 1,408 results