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1.
All the results given in the paper hold true. In the proof of Theorem 1, change steps IV, V, and VI to IV. for every , add to P; V. for every , add , , , , , to P; VI. for every , add to P.  相似文献   

2.
Constant-time distributed dominating set approximation   总被引:1,自引:0,他引:1  
Finding a small dominating set is one of the most fundamental problems of classical graph theory. In this paper, we present a new fully distributed approximation algorithm based on LP relaxation techniques. For an arbitrary, possibly constant parameter k and maximum node degree , our algorithm computes a dominating set of expected size in rounds. Each node has to send messages of size . This is the first algorithm which achieves a non-trivial approximation ratio in a constant number of rounds.Received: 9 September 2003, Accepted: 2 September 2004, Published online: 13 January 2005The work presented in this paper was supported (in part) by the National Competence Center in Research on Mobile Information and Communication Systems (NCCR-MICS), a center supported by the Swiss National Science Foundation under grant number 5005-67322.  相似文献   

3.
We give a complete characterization of the complexity of the element distinctness problem for n elements of bits each on deterministic and nondeterministic one-tape Turing machines. We present an algorithm running in time for deterministic machines and nondeterministic solutions that are of time complexity . For elements of logarithmic size , on nondeterministic machines, these results close the gap between the known lower bound and the previous upper bound . Additional lower bounds are given to show that the upper bounds are optimal for all other possible relations between m and n. The upper bounds employ hashing techniques, while the lower bounds make use of the communication complexity of set disjointness.Received: 23 April 2001, Published online: 2 September 2003Holger Petersen: Supported by Deutsche Akademie der Naturforscher Leopoldina, grant number BMBF-LPD 9901/8-1 of Bundesministerium für Bildung und Forschung.  相似文献   

4.
This paper investigates two preemptive semi-online scheduling problems to minimize makespan on two uniform machines. In the first semi-online problem, we know in advance that all jobs have their processing times in between p and rp . In the second semi-online problem, we know the size of the largest job in advance. We design an optimal semi-online algorithm which is optimal for every combination of machine speed ratio and job processing time ratio for the first problem, and an optimal semi-online algorithm for every machine speed ratio for the second problem.Received: 2 December 2003, Published online: 16 January 2004This research is supported by the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE, China, and National Natural Science Foundation of China (10271110).  相似文献   

5.
Fast allocation and deallocation with an improved buddy system   总被引:1,自引:0,他引:1  
We propose several modifications to the binary buddy system for managing dynamic allocation of memory blocks whose sizes are powers of two. The standard buddy system allocates and deallocates blocks in time in the worst case (and on an amortized basis), where n is the size of the memory. We present three schemes that improve the running time to O(1) time, where the time bound for deallocation is amortized for the first two schemes. The first scheme uses just one more word of memory than the standard buddy system, but may result in greater fragmentation than necessary. The second and third schemes have essentially the same fragmentation as the standard buddy system, and use bits of auxiliary storage, which is but for all and . Finally, we present simulation results estimating the effect of the excess fragmentation in the first scheme.Received: 4 May 2003, Published online: 22 December 2004Gerth Stølting Brodal: Supported by the Carlsberg Foundation (contract number ANS-0257/20). Partially supported by the Future and Emerging Technologies Programme of the EU under contract number IST-1999-14186 (ALCOM-FT). Basic Research in Computer Science, www.brics.dk, funded by the Danish National Research Foundation.Erik D. Demaine: Partially supported by the Natural Science and Engineering Research Council of Canada (NSERC).J. Ian Munro: Supported by the Natural Science and Engineering Research Council of Canada (NSERC) and the Canada Research Chair in Algorithm Design.This paper includes several results that appeared in preliminary form in the Proceedings of the 19th Conference on the Foundations of Software Technology and Theoretical Computer Science (FST & TCS99) [8].  相似文献   

6.
A graph G with n vertices and maximum degree cannot be given weak sense of direction using less than colours. It is known that n colours are always sufficient, and it was conjectured that just are really needed, that is, one more colour is sufficient. Nonetheless, it has been shown [3] that for sufficiently large n there are graphs requiring more colours than . In this paper, using recent results in asymptotic graph enumeration, we show that (surprisingly) the same bound holds for regular graphs. We also show that colours are necessary, where d G is the degree of G.Received: April 2002, Accepted: April 2003, Sebastiano Vigna: Partially supported by the Italian MURST (Finanziamento di iniziative di ricerca diffusa condotte da parte di giovani ricercatori).The results of this paper appeared in a preliminary form in Distributed Computing. 14th International Conference, DISC 2000, Springer-Verlag, 2000.  相似文献   

7.
Abstract  We obtain a multivariate extension of a classical result of Schoenberg on cardinal spline interpolation. Specifically, we prove the existence of a unique function in , polyharmonic of order p on each strip , , and periodic in its last n variables, whose restriction to the parallel hyperplanes , , coincides with a prescribed sequence of n-variate periodic data functions satisfying a growth condition in . The constructive proof is based on separation of variables and on Micchelli’s theory of univariate cardinal -splines. Keywords: cardinal -splines, polyharmonic functions, multivariable interpolation Mathematics Subject Classification (2000): 41A05, 41A15, 41A63  相似文献   

8.
The condition-based approach for consensus solvability consists of identifying sets of input vectors, called conditions, for which there exists an asynchronous protocol solving consensus despite the occurrence of up to f process crashes. This paper investigates , the largest set of conditions which allow us to solve the consensus problem in an asynchronous shared memory system.The first part of the paper shows that is made up of a hierarchy of classes of conditions, where d is a parameter (called degree of the condition), starting with and ending with d = 0, where . We prove that each one is strictly contained in the previous one: . Various properties of the hierarchy are also derived. It is shown that a class can be characterized in two equivalent but complementary ways: one is convenient for designing protocols while the other is for analyzing the class properties. The paper also defines a linear family of conditions that can be used to derive many specific conditions. In particular, for each d, two natural conditions are presented.The second part of the paper is devoted to the design of efficient condition-based protocols. A generic condition-based protocol is presented. This protocol can be instantiated with any condition C, , and requires at most shared memory read/write operations per process in the synchronization part of the protocol. Thus, the value (f-d) represents the difficulty of the class . An improvement of the protocol for the conditions in is also presented.Received: 15 November 2001, Accepted: 15 April 2003, Published online: 6 February 2004Parts of it have previously appeared in [23] and [25].  相似文献   

9.
In this paper, a method for matching complex objects in line-drawings is presented. Our approach is based on the notion of -signatures, which are a special kind of histogram of forces [17,19,28]. Such histograms have low time complexity and describe signatures that are invariant to fundamental geometrical transformations such as scaling, translation, symmetry, and rotation. This article presents a new application of this notion in the field of symbol identification and recognition. To improve the efficiency of matching, we propose using an approximation of the -signature from Fourier series and the associated matching.Received: 7 October 2002, Accepted: 1 December 2002, Published online: 4 July 2003  相似文献   

10.
The applicability of the accommodating function, a relatively new measure for the quality of on-line algorithms, is extended.The standard quality measure for on-line algorithms is the competitive ratio, which is, roughly speaking, the worst case ratio of the on-line performance to the optimal off-line performance. However, for many on-line problems, the competitive ratio gives overly pessimistic results and/or fails to distinguish between algorithms that are known to perform very differently in practice. Many researchers have proposed variations on the competitive ratio to obtain more realistic results. These variations are often tailor-made for specific on-line problems.The concept of the accommodating function applies to any on-line problem with some limited resource, such as bins, seats in a train, or pages in a cache. If a limited amount n of some resource is available, the accommodating function is the competitive ratio when input sequences are restricted to those for which the amount of resources suffices for an optimal off-line algorithm. For all resource bounded problems, the standard competitive ratio is .The accommodating function was originally used only for . We focus on , observe that the function now appears interesting for a greater variety of problems, and use it to make new distinctions between known algorithms and to find new ones.Received: 17 September 2002 / 12 June 2003Supported in part by the IST Programme of the EU under contract number IST-1999-14186 (ALCOM-FT) and in part by the Danish Natural Science Research Council (SNF).A preliminary version of this paper appeared in the Eighth Annual International Computing and Combinatorics Conference, Lecture Notes in Computer Science 2387: 87-96, Springer-Verlag, 2002.  相似文献   

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