Fundamentals of Engineering Thermodynamics (Solutions by Moran M. J., Shapiro H. N.

By Moran M. J., Shapiro H. N.

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Finally, we consider a hybrid algorithm obtained by combining the two different approaches used in [1, 2] and [3, 4] with running time O(m2 n2 ), and compare the implementations. The new algorithm is motivated by our need to reduce the cost of the shortest path computations. The resulting algorithm seems to be very efficient in practice for random dense unweighted graphs. Finally, we compare our implementations with previous implementations of minimum cycle basis algorithms [3, 8]. The paper is organized as follows.

In Proceedings of the 1st ACM International Workshop on Performance Evaluation of Wireless, Ad Hoc, Sensor and Ubiquitous Networks (PE-WASUN), pages 61–68. ACM Press, 2004. 10. P. J. Wan, G. Calinescu, X. Li, and O. Frieder. Minimum energy broadcasting in static ad hoc wireless networks. Wireless Networks, 8(6):607–617, 2002. Extended abstract appeared in Proceedings of the 20th Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM) (2001). 11. J. E. Wieselthier, G.

Sets are considered during the whole execution of the algorithm. Column # S, C = 1 denotes the number of updates performed on the sets S. An upper bound on this is N (N − 1)/2, which we actually use when bounding the algorithm’s running time. 5 10 22 13 25 150 126 75 1387 1313 150 5587 5438 200 9950 9751 300 22425 22126 500 62375 61876 N (N − 1)/2 max(|S|) avg(|S|) # S, C = 1 45 5778 124750 484620 2214460 10235550 4 44 226 425 1051 2218 2 4 7 7 13 17 8 258 2604 5469 20645 58186 6 2145 286903 5128003 16649335 86533590 681746275 2 27 370 1535 2849 6398 18688 2 3 6 9 10 10 14 2 137 3707 22239 49066 116084 455620 78 7875 861328 14783203 47536125 244768875 1914288750 7 57 654 2729 4769 10992 30983 2 4 6 9 11 13 15 14 363 6282 39292 86386 227548 837864 decrease does not concern the shortest path computations.

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