Results 11 - 20 of 22

On the Hardness of Approximating k-Dimensional Matching

by E. Hazan, S. Safra, O. Schwartz
"... We study bounded degree graph problems, mainly the problem of k-Dimensional Matching (k-DM), namely, the problem of finding a maximal matching in a k-partite k-uniform balanced hyper-graph. We prove that k-DM cannot be e#ciently approximated to within a factor of O( ) unless P = NP . This impro ..."
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We study bounded degree graph problems, mainly the problem of k-Dimensional Matching (k-DM), namely, the problem of finding a maximal matching in a k-partite k-uniform balanced hyper-graph. We prove that k-DM cannot be e#ciently approximated to within a factor of O( ) unless P = NP

On a hypergraph Turán problem of Frankl

by Peter Keevash, Benny Sudakov , 2002
"... Let C (2k) r be the 2k-uniform hypergraph obtained by letting P1, · · · , Pr be pairwise disjoint sets of size k and taking as edges all sets Pi ∪Pj with i ̸ = j. This can be thought of as the ‘k-expansion’ of the complete graph Kr: each vertex has been replaced with a set of size k. An example ..."
Abstract - Cited by 6 (1 self) - Add to MetaCart
of a hypergraph with vertex set V that does not contain C (2k) 3 can be obtained by partitioning V = V1∪V2 and taking as edges all sets of size 2k that intersect each of V1 and V2 in an odd number of elements. Let B (2k) n denote a hypergraph on n vertices obtained by this construction that has as many

Linear equation, arithmetic progressions and hypergraph property testing

by Noga Alon, Asaf Shapira - Proc. of the 16 th Annual ACM-SIAM SODA, ACM Press , 2005
"... For a fixed k-uniform hypergraph D (k-graph for short, k ≥ 3), we say that a k-graph H) if it contains no copy (resp. induced copy) of D. Our goal in satisfies property PD (resp. P ∗ D this paper is to classify the k-graphs D for which there are property-testers for testing PD and P ∗ D whose query ..."
Abstract - Cited by 7 (2 self) - Add to MetaCart
to obtain better lower bounds for any large enough k-graph. These results extend and improve previous results about graphs [5] and k-graphs [18]. For PD, we show that for any k-partite k-graph D, PD is easily testable, by giving an efficient one-sided error-property tester, which improves the one obtained

Connections - Magic Squares, Cubes and Matchings

by Marian Trenkler , 2001
"... The paper is a survey on magic squares, cubes, magic graphs, hypergraphs and matching in graph theory. The author gave some connections between these terms. Magic squares fascinated people throughour centuries. In 1686, Adamas Kochansky extended magic squares to three dimensions. In the paper M.Tren ..."
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.Sandorova and M.Trenkler gave its characterization. From their papers it follows connestion between magic graphs and matchings in graphs. There is a similar connestion is between a magic p-dimensional cube and a supermagic complete k-partite hypergraph.

Approximate Hypergraph Coloring under Low-discrepancy and Related Promises

by Vijay Bhattiprolu, et al.
"... A hypergraph is said to be χ-colorable if its vertices can be colored with χ colors so that no hyper-edge is monochromatic. 2-colorability is a fundamental property (called Property B) of hypergraphs and is extensively studied in combinatorics. Algorithmically, however, given a 2-colorable k-uniform ..."
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)) fraction of the hyperedges when ` = O(logk) (resp. ` = 2). Assuming the Unique Games conjecture, we improve the latter hardness factor to 2−O(k) for almost discrepancy-1 hypergraphs. • Rainbow colorability: If the hypergraph has a (k − `)-coloring such that each hyperedge is poly-chromatic with all

Hardness of Submodular Cost Allocation: Lattice Matching and a Simplex Coloring Conjecture

by Alina Ene, Jan Vondrák
"... We consider the Minimum Submodular Cost Allocation (MSCA) problem [3]. In this problem, we are given k submodular cost functions f1,..., fk: 2V → R+ and the goal is to partition V into k sets A1,..., Ak so as to minimize the total cost ∑k i=1 fi(Ai). We show that MSCA is inapproximable within any mu ..."
Abstract - Cited by 1 (0 self) - Add to MetaCart
We consider the Minimum Submodular Cost Allocation (MSCA) problem [3]. In this problem, we are given k submodular cost functions f1,..., fk: 2V → R+ and the goal is to partition V into k sets A1,..., Ak so as to minimize the total cost ∑k i=1 fi(Ai). We show that MSCA is inapproximable within any

Kernelization of Packing Problems

by Holger Dell, Dániel Marx , 2011
"... Kernelization algorithms are polynomial-time reductions from a problem to itself that guarantee their output to have a size not exceeding some bound. For example, d-Set Matching for integers d ≥ 3 is the problem of nding a matching of size at least k in a given d-uniform hypergraph and has kernels w ..."
Abstract - Cited by 20 (2 self) - Add to MetaCart
of three edges each. This does not quite match the best lower bound of O(k 2−ɛ) that we can prove. Most of our lower bound proofs follow a general scheme that we discover: To exclude kernels of size O(k d−ɛ) for a problem in d-uniform hypergraphs, one should reduce from a carefully chosen d-partite problem

Exact covers via determinants

by Andreas Björklund - In Proceedings of the 27th International Symposium on Theoretical Aspects of Computer Sciences, STACS 2010 , 2010
"... Given a k-uniform hypergraph on n vertices, partitioned in k equal parts such that every hyperedge includes one vertex from each part, the k-dimensional matching problem asks whether there is a disjoint collection of the hyperedges which covers all vertices. We show it can be solved by a randomized ..."
Abstract - Cited by 4 (1 self) - Add to MetaCart
Given a k-uniform hypergraph on n vertices, partitioned in k equal parts such that every hyperedge includes one vertex from each part, the k-dimensional matching problem asks whether there is a disjoint collection of the hyperedges which covers all vertices. We show it can be solved by a randomized

FACTORS IN RANDOM GRAPHS

by Anders Johansson, Jeff Kahn, Van Vu , 803
"... Abstract. Let H be a fixed graph on v vertices. For an n-vertex graph G with n divisible by v, an H-factor of G is a collection of n/v copies of H whose vertex sets partition V (G). In this paper we consider the threshold thH(n) of the property that an Erdős-Rényi random graph (on n points) contains ..."
Abstract - Cited by 1 (0 self) - Add to MetaCart
) contains an H-factor. Our results determine thH(n) for all strictly balanced H. The method here extends with no difficulty to hypergraphs. As a corollary, we obtain the threshold for a perfect matching in random k-uniform hypergraph, solving the well-known “Shamir’s problem.” 1.

Load Balancing Issues in Super-Peer-based Publish/Subscribe Digital

by Libraries Ioannis Christou , 2005
"... We present a hyper-graph partitioning based approach to the problem of load-balancing in largescale P2P-based digital libraries. In such libraries, in addition to publishing digital content, peer-clients may subscribe their intent to be notified whenever digital content matching appropriate meta-dat ..."
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We present a hyper-graph partitioning based approach to the problem of load-balancing in largescale P2P-based digital libraries. In such libraries, in addition to publishing digital content, peer-clients may subscribe their intent to be notified whenever digital content matching appropriate meta
Results 11 - 20 of 22