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1.
We consider the problem of characterizing user equilibria and optimal solutions for selfish routing in a given network. We extend the known models by considering malicious behavior. While selfish users follow a strategy that minimizes their individual cost, a malicious user will use his flow through the network in an effort to cause the maximum possible damage to the overall cost. We define a generalized model, present characterizations of flows at equilibrium and prove bounds for the ratio of the social cost of a flow at equilibrium over the cost when centralized coordination among users is allowed. An extended abstract of this work appeared in the Proceedings of the 14th Annual International Symposium on Algorithms and Computation (ISAAC) 2003. G. Karakostas’ research was supported by an NSERC Discovery research grant and MITACS. Part of this research was done when Viglas was a postdoctoral fellow at the University of Toronto, Canada.  相似文献   

2.
Fast matrix multiplication is stable   总被引:1,自引:1,他引:0  
We perform forward error analysis for a large class of recursive matrix multiplication algorithms in the spirit of Bini and Lotti [Numer. Math. 36:63–72, 1980]. As a consequence of our analysis, we show that the exponent of matrix multiplication (the optimal running time) can be achieved by numerically stable algorithms. We also show that new group-theoretic algorithms proposed in Cohn and Umans [Foundations of Computer Science, 44th Annual IEEE Symposium, pp. 438–449, 2003] and Cohn et al. [Foundations of Computer Science, 46th Annual IEEE Symposium, pp. 379–388, 2005] are all included in the class of algorithms to which our analysis applies, and are therefore numerically stable. We perform detailed error analysis for three specific fast group-theoretic algorithms. J. Demmel acknowledges support of NSF under grants CCF-0444486, ACI-00090127, CNS-0325873 and of DOE under grant DE-FC02-01ER25478. I. Dumitriu acknowledges support of the Miller Institute for Basic Research in Science. R. Kleinberg is supported by an NSF Mathematical Sciences Postdoctoral Research Fellowship  相似文献   

3.
Nishimura et al. [On graph powers for leaf-labeled trees, J. Algorithms 42 (2002) 69-108] define a k-leaf root of a graph G=(VG,EG) as a tree T=(VT,ET) such that the vertices of G are exactly the leaves of T and two vertices in VG are adjacent in G if and only if their distance in T is at most k. Solving a problem posed by Niedermeier [Personal communication, May 2004] we give a structural characterization of the graphs that have a 4-leaf root. Furthermore, we show that the graphs that have a 3-leaf root are essentially the trees, which simplifies a characterization due to Dom et al. [Error compensation in leaf power problems, Algorithmica 44 (2006) 363-381. (A preliminary version appeared under the title “Error compensation in leaf root problems”, in: Proceedings of the 15th Annual International Symposium on Algorithms and Computation (ISAAC 2004), Lecture Notes in Computer Science, vol. 3341, pp. 389-401)] and also a related recognition algorithm due to Nishimura et al. [On graph powers for leaf-labeled trees, J. Algorithms 42 (2002) 69-108].  相似文献   

4.
We show the existence of a fully polynomial-time approximation scheme (FPTAS) for the problem of maximizing a non-negative polynomial over mixed-integer sets in convex polytopes, when the number of variables is fixed. Moreover, using a weaker notion of approximation, we show the existence of a fully polynomial-time approximation scheme for the problem of maximizing or minimizing an arbitrary polynomial over mixed-integer sets in convex polytopes, when the number of variables is fixed. A conference version of this article, containing a part of the results presented here, appeared in Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms, Miami, FL, January 22–24, 2006, pp. 743–748. The first author gratefully acknowledges support from NSF grant DMS-0608785, a 2003 UC-Davis Chancellor’s fellow award, the Alexander von Humboldt foundation, and IMO Magdeburg. The remaining authors were supported by the European TMR network ADONET 504438.  相似文献   

5.
Arc-annotated sequences are useful in representing the structural information of RNA and protein sequences. The

problem has recently been introduced in [P.A. Evans, Algorithms and complexity for annotated sequence analysis, PhD Thesis, University of Victoria, 1999; P.A. Evans, Finding common subsequences with arcs and pseudoknots, in: Proceedings of 10th Annual Symposium on Combinatorial Pattern Matching (CPM'99), in: Lecture Notes in Comput. Sci., vol. 1645, 1999, pp. 270–280] as a framework for studying the similarity of arc-annotated sequences. In this paper, we consider arc-annotated sequences with various arc structures and present some new algorithmic and complexity results on the problem. Some of our results answer an open question in [P.A. Evans, Algorithms and complexity for annotated sequence analysis, PhD Thesis, University of Victoria, 1999; P.A. Evans, Finding common subsequences with arcs and pseudoknots, in: Proceedings of 10th Annual Symposium on Combinatorial Pattern Matching (CPM'99), in: Lecture Notes in Comput. Sci., vol. 1645, 1999, pp. 270–280] and some others improve the hardness results in [P.A. Evans, Algorithms and complexity for annotated sequence analysis, PhD Thesis, University of Victoria, 1999; P.A. Evans, Finding common subsequences with arcs and pseudoknots, in: Proceedings of 10th Annual Symposium on Combinatorial Pattern Matching (CPM'99), in Lecture Notes in Comput. Sci., vol. 1645, 1999, pp. 270–280].  相似文献   

6.
We apply the Column Construction Method (Varadarajan et al., Proceedings of the Fifteenth Annual ACM-SIAM Symposium On Discrete Algorithms, pp. 562–571, 2004) to a minimal clique cover of an interval graph to obtain a new proof that First-Fit is 8-competitive for online coloring interval graphs. This proof also yields a new discovery that in each minimal clique cover of an interval graph G, there is a clique of size .  相似文献   

7.
In this paper, the compound Poisson risk model with surplus-dependent premium rate is analyzed in the taxation system proposed by Albrecher and Hipp (Bl?tter der DGVFM 28(1):13–28, 2007). In the compound Poisson risk model, Albrecher and Hipp (Bl?tter der DGVFM 28(1):13–28, 2007) showed that a simple relationship between the ruin probabilities in the risk model with and without tax exists. This so-called tax identity was later generalized to a surplus-dependent tax rate by Albrecher et al. (Insur Math Econ 44(2):304–306, 2009). The present paper further generalizes these results to the Gerber–Shiu function with a generalized penalty function involving the maximum surplus prior to ruin. We show that this generalized Gerber–Shiu function in the risk model with tax is closely related to the ‘original’ Gerber–Shiu function in the risk model without tax defined in a dividend barrier framework. The moments of the discounted tax payments before ruin and the optimal threshold level for the tax authority to start collecting tax payments are also examined.  相似文献   

8.
The average-case analysis of algorithms usually assumes independent, identical distributions for the inputs. In [C. Kenyon, Best-fit bin-packing with random order, in: Proc. of the Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, 1996, pp. 359–364] Kenyon introduced the random-order ratio, a new average-case performance metric for bin packing heuristics, and gave upper and lower bounds for it for the Best Fit heuristics. We introduce an alternative definition of the random-order ratio and show that the two definitions give the same result for Next Fit. We also show that the random-order ratio of Next Fit equals to its asymptotic worst-case, i.e., it is 2.  相似文献   

9.
This paper describes new improvements for BB-MaxClique (San Segundo et al. in Comput Oper Resour 38(2):571–581, 2011), a leading maximum clique algorithm which uses bit strings to efficiently compute basic operations during search by bit masking. Improvements include a recently described recoloring strategy in Tomita et al. (Proceedings of the 4th International Workshop on Algorithms and Computation. Lecture Notes in Computer Science, vol 5942. Springer, Berlin, pp 191–203, 2010), which is now integrated in the bit string framework, as well as different optimization strategies for fast bit scanning. Reported results over DIMACS and random graphs show that the new variants improve over previous BB-MaxClique for a vast majority of cases. It is also established that recoloring is mainly useful for graphs with high densities.  相似文献   

10.
We consider all-optical networks that use wavelength-division multiplexing and employ wavelength conversion at specific nodes in order to maximize their capacity usage. We investigate the effect of allowing reroutings on the number of necessary wavelength converters. We disprove a claim of Wilfong and Winkler [G. Wilfong, P. Winkler, Ring routing and wavelength translation, in: Proceedings of the 9th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA ’98, 1998, pp. 333-341] according to which reroutings do not have any effect on the number of necessary wavelength converters on bidirected networks. We show that there exist (bidirected) networks on n nodes that require Θ(n) converters without reroutings, but only O(1) converters if reroutings are allowed. We also address the cases of undirected networks and networks with shortest-path routings. In each case, we resolve the complexity of computing optimal placements of converters.  相似文献   

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