منابع مشابه
Longest Path Distance in Random Circuits
We study distance properties of a general class of random directed acyclic graphs (DAGs). In a DAG, many natural notions of distance are possible, for there exists multiple paths between pairs of nodes. The distance of interest for circuits is the maximum length of a path between two nodes. We give laws of large numbers for the typical depth (distance to the root) and the minimum depth in a ran...
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Due to the importance of longest path analysis in networks of queues, we develop an analytical method for computing the steady-state distribution function of longest path in acyclic networks of queues. We assume the network consists of a number of queuing systems and each one has either one or infinite servers. The distribution function of service time is assumed to be exponential or Erlang. Fu...
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Consider a weighted or unweighted k-nearest neighbor graph that has been built on n data points drawn randomly according to some density p on R. We study the convergence of the shortest path distance in such graphs as the sample size tends to infinity. We prove that for unweighted kNN graphs, this distance converges to an unpleasant distance function on the underlying space whose properties are...
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We consider the so-called Path Partition Conjecture for digraphs which states that for every digraph, D, and every choice of positive integers, λ1, λ2, such that λ1 + λ2 equals the order of a longest directed path in D, there exists a partition of D into two digraphs, D1 and D2, such that the order of a longest path in Di is at most λi, for i = 1, 2. We prove that certain classes of digraphs, w...
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Culberson and Rudnicki [J.C. Culberson, P. Rudnicki, A fast algorithm for constructing trees from distance matrices, Inform. Process. Lett. 30 (4) (1989) 215–220] gave an algorithm that reconstructs a degree d restricted tree from its distance matrix. According to their analysis, it runs in time O(dn logd n) for topological trees. However, this turns out to be false; we show that the algorithm ...
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ژورنال
عنوان ژورنال: Combinatorics, Probability and Computing
سال: 2012
ISSN: 0963-5483,1469-2163
DOI: 10.1017/s0963548312000260