Topic
Disjoint sets
About: Disjoint sets is a research topic. Over the lifetime, 12145 publications have been published within this topic receiving 183313 citations. The topic is also known as: disjoint set & mutually exclusive sets.
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TL;DR: A hybrid descent method is proposed for solving a special case of the well-known network design problem with relays, that is, the two-edge disjoint survivable network design Problem with Relays, where its provided results are compared to those reached by the best methods available in the literature.
1 citations
TL;DR: The expected number of FSTs spanning exactly K terminals and satisfying the empty lune property, a weak version of the bottleneck property, and the so-called empty hyperbox property is O(n(log log n)2(d-1)) for K = 3, assuming terminals are randomly distributed in a hypercube with a uniform distribution.
Abstract: Given a finite set Z of n points, called terminals, in Rd, the Rectilinear Steiner Tree Problem asks for a tree of minimal L1-length spanning Z. An optimal solution has a unique decomposition into full Steiner trees (FSTs). By using geometric properties and combinatorial arguments, we bound the expected number of FSTs satisfying simple necessary conditions for being part of an optimal solution. More specifically, we show that the expected number of FSTs spanning exactly K terminals and satisfying the empty lune property, a weak version of the bottleneck property, and the so-called empty hyperbox property is O(n(log log n)2(d-1)) for K = 3 and O(n(log log n)d-1 log K-2n) for K > 3, assuming terminals are randomly distributed in a hypercube with a uniform distribution. In the plane, we improve an earlier bound by showing that the expected number of FSTs with the Hwang form spanning exactly K terminals and satisfying the empty lune property and the so-called disjoint lunes property is O(nπK). © 2009 Wiley Periodicals, Inc. NETWORKS, 2010
1 citations
Patent•
25 Aug 2017TL;DR: In this article, the composed policy graph is divided into a plurality of sub-graphs, each subgraph comprising a plurality with edges and nodes that the edges are connected to.
Abstract: Example method includes: receiving, by a network device, a plurality of input policy graphs and a composed policy graph associated with the input policy graphs; dividing the composed policy graph into a plurality of sub-graphs, each sub-graph comprising a plurality of edges and a plurality of source nodes and destination nodes that the edges are connected to; selecting a first subset of sub-graphs that include, as a source node, a disjoint part of an original source EPG for each input policy graph; identifying a second subset within the first subset of sub-graphs that include, as a destination node, a disjoint part of an original destination EPG for the each input policy graph; and verifying whether connectivity in the composed policy graph reflects a corresponding policy in the plurality of input policy graphs for each sub-graph in the second subset.
1 citations
TL;DR: A pair of disjoint 3-GDDs of type gtu1 are studied and it is established that its necessary conditions are also sufficient to construct some optimal constant-weight codes.
Abstract: Pairwise disjoint 3-GDDs can be used to construct some optimal constant-weight codes. We study the existence of a pair of disjoint 3-GDDs of type g t u 1 and establish that its necessary conditions are also sufficient.
1 citations