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An ordered graph is a pair G = (G,≺) where G is a graph and ≺ is a total ordering of its vertices. The ordered Ramsey number R(G) is the minimum number N such that every ordered complete graph with N vertices and with edges colored by two colors contains a monochromatic copy of G. We show that for every integer d ≥ 3, almost every d-regular graph G satisfies R(G) ≥ n3/2−1/d 4 log n log log n fo...

This paper presents efficient multicasting with reduced contention on irregular networks with switchbased wormhole interconnection and unicast message passing. First, it is proved that for an arbitrary irregular network with a typical deadlock-free, adaptive routing, it may not be possible to create an ordered list of nodes to implement an arbitrary multicast in a contention-free manner with mi...

It is well known that every bipartite graph with vertex classes of size nwhose minimum degree is at least n/2 contains a perfect matching. We prove an analogue of this result for uniform hypergraphs. We also provide an analogue of Dirac’s theorem on Hamilton cycles for 3-uniform hypergraphs: We say that a 3-uniform hypergraph has a Hamilton cycle if there is a cyclic ordering of its vertices su...

Many graph problems require us to find subgraphs satisfying constraints such as no cycle, connected, degree-bounded and so on. Frontier-based search is a framework to construct a compressed data structure ZDD storing all subgraphs satisfying constraints in a given graph. Since frontier-based search processes edges one by one in a given order, we should determine an edge order of a given graph a...

We present a novel analysis of the potential effectiveness of a matrix ordering for IC in terms of just the sparsity structure. By looking at the structure of the approximate inverse implicitly created by IC we can help to explain the success of Reverse Cuthill-McKee orderings, the problems IC(0) has under Red-Black orderings that disappear when extra fill is included, and where fill must be ad...

In 1991 I described a particularly simple and elegant watershed algorithm, where the ooding a topographic surface was scheduled by a hierarchical queue. In 2004 the watershed line has been described as the skeleton by zone of in uence for the topographic distance. The same algorithm still applies. In 2012 I de ned a new distance based on a lexicographic ordering of the downstream paths leading ...

many ranking methods have been proposed so far. however, there is yet no method that can always give a satisfactory solution to every situation; some are counterintuitive, not discriminating; some use only the local information of fuzzy values; some produce different ranking for the same situation. for overcoming the above problems, we propose a new method for ranking fuzzy quantities based on ...

The impact of thin film confinement on the ordering of lamellae was investigated using symmetric poly(styrene-b-[isoprene-ran-epoxyisoprene]) diblock copolymers bound by nonpreferential wetting interfaces. The order-disorder transition temperature (TODT) and the occurrence of composition fluctuations in the disordered state are not significantly affected by two-dimensional confinement. Directed...

This paper presents eecient multicasting with reduced contention on irregular networks with switch-based wormhole interconnection and unicast message passing. First, it is proved that for an arbitrary irregular network with a typical deadlock-free, adaptive routing, it may not be possible to create an ordered list of nodes to implement an arbitrary multicast in a contention-free manner with min...