In this paper we analyze the expected time complexity of the auction algorithm for the matching problem on random bipartite graphs. We first prove that if for every non-maximum matching on graph G there exist an augme...
详细信息
In this paper we analyze the expected time complexity of the auction algorithm for the matching problem on random bipartite graphs. We first prove that if for every non-maximum matching on graph G there exist an augmenting path with a length of at most 2l + 1 then the auction algorithm converges after N . l iterations at most. Then, we prove that the expected time complexity of the auction algorithm for bipartite matching on random graphs with edge probability p = c log(N) N and c > 1 is O (N log(2)(N)/log(Np)) w.h.p. This time complexity is equal to other augmenting path algorithms such as the HK algorithm. Furthermore, we show that the algorithm can be implemented on parallel machines with O(log(N)) processors and shared memory with an expected time complexity of O(N log(N)). (c) 2014 Wiley Periodicals, Inc.
To determine the stability of LEGO (R) structures is an interesting problem because the special binding mechanism prohibits the usage of methods of structural frame design or dynamic physics engines. We propose a new ...
详细信息
ISBN:
(纸本)9783642330902
To determine the stability of LEGO (R) structures is an interesting problem because the special binding mechanism prohibits the usage of methods of structural frame design or dynamic physics engines. We propose a new two-phase approach where instances of maximum-flow networks are constructed. In a first phase, the distribution of compressive and tensile forces is computed which is used in a second phase to model the moments within the structure. By solving the maximum-flow networks we can use the resulting flow as a sufficient criterion for the stability of the structure. The approach is demonstrated for two exemplary structures which outperform previous results using a multi-commodity flow network.
暂无评论