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31.
32.
We consider the issue of sampling from the posterior distribution of exponential random graph (ERG) models and other statistical models with intractable normalizing constants. Existing methods based on exact sampling are either infeasible or require very long computing time. We study a class of approximate Markov chain Monte Carlo (MCMC) sampling schemes that deal with this issue. We also develop a new Metropolis–Hastings kernel to sample sparse large networks from ERG models. We illustrate the proposed methods on several examples. 相似文献
33.
图的染色理论是图论的一个重要分支。本文使用分析的方法得到了轮和完全等二部图联图的全色数、均匀全色数和邻点可区别边色数。 相似文献
34.
Koen Jochmans 《商业与经济统计学杂志》2013,31(4):705-713
ABSTRACTWe consider a statistical model for directed network formation that features both node-specific parameters that capture degree heterogeneity and common parameters that reflect homophily among nodes. The goal is to perform statistical inference on the homophily parameters while treating the node-specific parameters as fixed effects. Jointly estimating all parameters leads to incidental-parameter bias and incorrect inference. As an alternative, we develop an approach based on a sufficient statistic that separates inference on the homophily parameters from estimation of the fixed effects. The estimator is easy to compute and can be applied to both dense and sparse networks, and is shown to have desirable asymptotic properties under sequences of growing networks. We illustrate the improvements of this estimator over maximum likelihood and bias-corrected estimation in a series of numerical experiments. The technique is applied to explain the import and export patterns in a dense network of countries and to estimate a more sparse advice network among attorneys in a corporate law firm. 相似文献
35.
Toshimasa Ishii Hiroshi Nagamochi Toshihide Ibaraki 《Journal of Combinatorial Optimization》2000,4(1):35-77
Given an undirected multigraph G = (V, E) and two positive integers and k, we consider the problem of augmenting G by the smallest number of new edges to obtain an -edge-connected and k-vertex-connected multigraph. In this paper, we show that the problem can be solved in Õ(mn2) time for any fixed and k = 3 if an input multigraph G is 2-vertex-connected, where n = |V| and m is the number of pairs of adjacent vertices in G. 相似文献
36.
We investigate the computational complexity of two special cases of the Steiner tree problem where the distance matrix is a Kalmanson matrix or a circulant matrix, respectively. For Kalmanson matrices we develop an efficient polynomial time algorithm that is based on dynamic programming. For circulant matrices we give an
-hardness proof and thus establish computational intractability. 相似文献
37.
Sorting by Reversals (SBR) is one of the most widely studied models of genome rearrangements in computational molecular biology. At present,
is the best known approximation ratio achievable in polynomial time for SBR. A very closely related problem, called Breakpoint Graph Decomposition (BGD), calls for a largest collection of edge disjoint cycles in a suitably-defined graph. It has been shown that for almost all instances SBR is equivalent to BGD, in the sense that any solution of the latter corresponds to a solution of the former having the same value. In this paper, we show how to improve the approximation ratio achievable in polynomial time for BGD, from the previously known
to
for any > 0. Combined with the results in (Caprara, Journal of Combinatorial Optimization, vol. 3, pp. 149–182, 1999b), this yields the same approximation guarantee for n! – O((n – 5)!) out of the n! instances of SBR on permutations with n elements. Our result uses the best known approximation algorithms for Stable Set on graphs with maximum degree 4 as well as for Set Packing where the maximum size of a set is 6. Any improvement in the ratio achieved by these approximation algorithms will yield an automatic improvement of our result. 相似文献
38.
Yoshiyuki Kusakari Daisuke Masubuchi Takao Nishizeki 《Journal of Combinatorial Optimization》2001,5(2):249-266
Let G = (V,E) be a plane graph with nonnegative edge weights, and let
be a family of k vertex sets
, called nets. Then a noncrossing Steiner forest for
in G is a set
of k trees
in G such that each tree
connects all vertices, called terminals, in net N
i, any two trees in
do not cross each other, and the sum of edge weights of all trees is minimum. In this paper we give an algorithm to find a noncrossing Steiner forest in a plane graph G for the case where all terminals in nets lie on any two of the face boundaries of G. The algorithm takes time
if G has n vertices and each net contains a bounded number of terminals. 相似文献
39.
The problem of computing the strength and performing optimal reinforcement for an edge-weighted graph G(V, E, w) is well-studied. In this paper, we present fast (sequential linear time and parallel logarithmic time) on-line algorithms for optimally reinforcing the graph when the reinforcement material is available continuously on-line. These are the first on-line algorithms for this problem. We invest O(|V|3|E|log|V|) time (equivalent to (|V|) invocations of the fastest known algorithms for optimal reinforcement) in preprocessing the graph before the start of our algorithms. It is shown that the output of our on-line algorithms is as good as that of the off-line algorithms. Thus our algorithms are better than the fastest off-line algorithms in situations when a sequence of more than (|V|) reinforcement problems need to be solved. The key idea is to make use of ideas underlying the theory of Principal Partition of a Graph. Our ideas are easily generalized to the general setting of polymatroid functions. We also present a new efficient algorithm for computation of the Principal Sequence of a graph. 相似文献
40.
Let k 5 be a fixed integer and let m = (k – 1)/2. It is shown that the independence number of a C
k-free graph is at least c
1[ d(v)1/(m – 1)](m – 1)/m
and that, for odd k, the Ramsey number r(C
k, K
n) is at most c
2(n
m + 1/log n)1/m
, where c
1 = c
1(m) > 0 and c
2 = c
2(m) > 0. 相似文献