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On the Hardness of Approximating kDimensional Matching
"... We study bounded degree graph problems, mainly the problem of kDimensional Matching (kDM), namely, the problem of finding a maximal matching in a kpartite kuniform balanced hypergraph. We prove that kDM cannot be e#ciently approximated to within a factor of O( ) unless P = NP . This impro ..."
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Cited by 25 (1 self)
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We study bounded degree graph problems, mainly the problem of kDimensional Matching (kDM), namely, the problem of finding a maximal matching in a kpartite kuniform balanced hypergraph. We prove that kDM cannot be e#ciently approximated to within a factor of O( ) unless P = NP
On a hypergraph Turán problem of Frankl
, 2002
"... Let C (2k) r be the 2kuniform 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 ‘kexpansion’ of the complete graph Kr: each vertex has been replaced with a set of size k. An example ..."
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Cited by 6 (1 self)
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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
 Proc. of the 16 th Annual ACMSIAM SODA, ACM Press
, 2005
"... For a fixed kuniform hypergraph D (kgraph for short, k ≥ 3), we say that a kgraph 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 kgraphs D for which there are propertytesters for testing PD and P ∗ D whose query ..."
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Cited by 7 (2 self)
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to obtain better lower bounds for any large enough kgraph. These results extend and improve previous results about graphs [5] and kgraphs [18]. For PD, we show that for any kpartite kgraph D, PD is easily testable, by giving an efficient onesided errorproperty tester, which improves the one obtained
Connections  Magic Squares, Cubes and Matchings
, 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 pdimensional cube and a supermagic complete kpartite hypergraph.
Approximate Hypergraph Coloring under Lowdiscrepancy and Related Promises
"... A hypergraph is said to be χcolorable if its vertices can be colored with χ colors so that no hyperedge is monochromatic. 2colorability is a fundamental property (called Property B) of hypergraphs and is extensively studied in combinatorics. Algorithmically, however, given a 2colorable kuniform ..."
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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 discrepancy1 hypergraphs. • Rainbow colorability: If the hypergraph has a (k − `)coloring such that each hyperedge is polychromatic with all
Hardness of Submodular Cost Allocation: Lattice Matching and a Simplex Coloring Conjecture
"... 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 ..."
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Cited by 1 (0 self)
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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
, 2011
"... Kernelization algorithms are polynomialtime reductions from a problem to itself that guarantee their output to have a size not exceeding some bound. For example, dSet Matching for integers d ≥ 3 is the problem of nding a matching of size at least k in a given duniform hypergraph and has kernels w ..."
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Cited by 20 (2 self)
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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 duniform hypergraphs, one should reduce from a carefully chosen dpartite problem
Exact covers via determinants
 In Proceedings of the 27th International Symposium on Theoretical Aspects of Computer Sciences, STACS 2010
, 2010
"... Given a kuniform hypergraph on n vertices, partitioned in k equal parts such that every hyperedge includes one vertex from each part, the kdimensional 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 ..."
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Cited by 4 (1 self)
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Given a kuniform hypergraph on n vertices, partitioned in k equal parts such that every hyperedge includes one vertex from each part, the kdimensional 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
, 803
"... Abstract. Let H be a fixed graph on v vertices. For an nvertex graph G with n divisible by v, an Hfactor 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 ErdősRényi random graph (on n points) contains ..."
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Cited by 1 (0 self)
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) contains an Hfactor. 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 kuniform hypergraph, solving the wellknown “Shamir’s problem.” 1.
Load Balancing Issues in SuperPeerbased Publish/Subscribe Digital
, 2005
"... We present a hypergraph partitioning based approach to the problem of loadbalancing in largescale P2Pbased digital libraries. In such libraries, in addition to publishing digital content, peerclients may subscribe their intent to be notified whenever digital content matching appropriate metadat ..."
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We present a hypergraph partitioning based approach to the problem of loadbalancing in largescale P2Pbased digital libraries. In such libraries, in addition to publishing digital content, peerclients may subscribe their intent to be notified whenever digital content matching appropriate meta
Results 11  20
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