Y. Bartal, A. Fiat, and S. Leonardi. Lower bounds for on-line graph problems with application to on-line circuit and optical routing. In Proceedings of the 28th Annual ACM Symposium on Theory of Computing, pages 531--540, 1996.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... Topology competitive ratio competitive ratio known using generic c competitive using best known competitive lower bounds for Oedpa algorithm for Oedpa algorithm for Oedpa (Oca with # = 1) arbitrary network with n nodes, O(# log n) on n n meshes randomized: n 1 log 4 3 [3] tree with n nodes, 12(c 1) #log ## 1) Theorem 3.2) 24 log n 2) line with n nodes, 8(c 1) #log ## 1) Corollary 3.7) 8#log n# 8) Table 1. Results in Online Call Admission in Optical Networks. The parameter #G is defined as max # s,t where # s,t ....

....is essentially the best which we can expect for deterministic algorithms. Theorem 2.2. On a line with n nodes, no deterministic algorithm for Oca can be c competitive with c #(n 1) Proof. The worst case sequence is a straightforward generalization of the known lower bound construction from [3] for Oedpa on the line with n nodes. Let the nodes be numbered by v 1 , v 2 , vn from left to right. The adversary first issues a request r 1 = v 1 , vn , 1) It is straightforward to see that any deterministic algorithm which achieves a finite competitive ratio must accept r 1 . The ....

Y. Bartal, A. Fiat, and S. Leonardi, Lower bounds for on-line graph problems with applications to on-line curcuit and optimal routing, Proceedings of the 28th Annual ACM Symposium on the Theory of Computing, 1996, pp. 531--540.

....of the available bandwidth. Note that for general networks one can achieve logarithmic competitive ratios by deterministic algorithms for requests of small bandwidth [5] while no poly logarithmic competitive ratio can be achieved for requests of full bandwidth even by randomized algorithms [9]. For special networks, e.g. trees, meshes, classes of planner graphs [6, 7, 15] it is possible to design logarithmic competitive algorithms for the call control problem without limiting the requested bandwidth. Nevertheless, we are not aware of any constant competitive algorithm for disjoint ....

Y. Bartal, A. Fiat, and S. Leonardi. Lower bounds for on-line graph problems with application to on-line circuit and optical routing. In Proc. 28th ACM Symp. on Theory of Computing, pages 531-540, 1996.

....can achieve a competitive ratio better than 2 while they mention the folklore Fixed Allocation algorithm which is 3 competitive. The static version of the call control problem is very similar to the famous maximum independent set problem. The on line version of the problem is studied in [1, 2, 3, 6, 11]. 1] 2] and [6] study the call control problem in the context of optical networks. Pantziou et al. 11] present upper bounds for planar and arbitrary mobile networks. Applying the Classify and Randomly Select paradigm [2, 11] on cellular networks, we obtain a 3 competitive randomized call ....

....focuses on networks supporting one frequency. Awerbuch et al. 1] present a simple way to tranform algorithms designed for one frequency to algorithms for arbitrarily many frequencies with a small sacrifice in competitiveness. Lower bounds for call control in arbitrary networks are presented in [3]. In this paper, we address the on line version of the frequency allocation and the call control problem. For frequency allocation in cellular networks, we improve the best known competitive ratio upper bound of 3 achieved by the Fixed Allocation algorithm [5] presenting an almost tight ....

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Y. Bartal, A. Fiat, and S. Leonardi. Lower Bounds for On--line Graph Problems with Applications to On--line Circuit and Optical Routing. In Proc. of the 28th Annual ACM Symposium on Theory of Computing (STOC '96), pp. 531--540, 1996.

....monotone set system M, where E( is the expectation over the player s random choices and OPT (s) maxM2M jM sj. Note that for every M, e(M) 2 [0; 1] and it is easy to show that a system has performance one iff it is a matroid. This model generalizes the apparently unrelated models in [2] and [3]. The video on demand problem studied in [1, 2] corresponds to the case when M is the monotone closure of l disjoint sets of size k. Let e(k; l) denote the performance of this set system. Awerbuch et al. 1] show that e(k; l) Omega Gamma1 = log k log l) We improve this bound for some values ....

....to zero. We also show, that if M = M 1 [ M l , and k is an upper bound on the size of the largest set in M, then the performance of M is at least as good as the performance of the worst of the components multiplied by a factor of e(k; l) Our model also generalizes one of Bartal et al. [3] who considered set systems that arise from hereditary graph properties. Bartal et al. use specific graph product to prove that for every n there exists a graph G with O(n) vertices such that the performance of the system of its independent sets is no greater than . Unfortunately their argument ....

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Y. Bartal, A. Fiat, and S. Leonardi. Lower bounds for on-line graph problems with application to online circuit and optical routing. In Proc. 28th ACM Symposium on Theory of Computing, pages 531--540, 1996.

....seems to be hard to approximate. If the size of the network, N , is the only parameter that is known, then the trivial deterministic lower bound of Omega Gamma N) for the line shows that there is no hope for deterministic algorithms with reasonable competitive ratio. Bartal, Fiat and Leonardi [6] prove this effort to be in vain even for randomized algorithms by giving an Omega Gamma N ffl ) lower bound for randomized on line algorithms on general networks, where ffl = 2=3 1 Gammalog 4 3 . When more parameters are known, the best known approximation ratios for arbitrary graphs are ....

Y. Bartal, A. Fiat, and S. Leonardi. Lower bounds for on-line graph problems with application to on-line circuit and optical routing. In Proceedings of the 28th Annual ACM Symposium on the Theory of Computing, pages 531--540, Philadelphia, Pennsylvania, 22--24 May 1996.

....[8] describe an algorithm with approximation ratio O( 2 2 log 3 n) In the on line setting, the trivial deterministic lower bound of n) for the line shows that in general there is no hope for on line deterministic algorithms with reasonable competitive ratio. Bartal, Fiat and Leonardi [7] prove this e ort to be in vain even for randomized algorithms by giving an n ) lower bound for randomized on line algorithms on general networks, where = 2 3 (1 log 4 3) As a consequence of these large lower bounds, research has mainly focused on speci c topologies. On line algorithms ....

Y. Bartal, A. Fiat, and S. Leonardi. Lower bounds for on-line graph problems with application to on-line circuit and optical routing. In Proc. of the 28th ACM Symposium on the Theory of Computing, pages 531-540, 1996.

....oblivious adversaries whose knowledge is limited to the probability distribution of the random choices of the randomized algorithm. The static version of the call control problem is very similar to the famous maximum independent set problem. The on line version of the problem is studied in [1, 2, 3, 4, 7, 9]. 1] 2] and [7] study the call control problem in the context of optical networks. Pantziou et al. 9] present upper bounds for planar and arbitrary mobile networks. Applying the CLASSIFY AND RANDOMLY SELECT paradigm [2, 9] on cellular networks, we obtain a 3 competitive randomized call ....

....focuses on networks supporting one frequency. Awerbuch et al. 1] present a simple way to transform algorithms designed for one frequency to algorithms for arbitrarily many frequencies with a small sacrifice in competitiveness. Lower bounds for call control in arbitrary networks are presented in [3]. The authors in [4] describe algorithm p RANDOM, an intuitive on line randomized call control algorithm for networks that support one frequency. Using simple arguments they prove an upper bound of 2:97 on its competitive ratio against oblivious adversaries. In this way they beat the barrier of ....

Y. Bartal, A. Fiat, and S. Leonardi. Lower Bounds for On--line Graph Problems with Applications to On-- line Circuit and Optical Routing. In Proc. of the 28th Annual ACM Symposium on Theory of Computing (STOC '96), 1996.

No context found.

Y. Bartal, A. Fiat, S. Leonardi. Lower bounds for on-line graph problems with application to on-line circuit and optical routing. In Proceedings of the 28th ACM Symposium on Theory of Computing, pages 531-540, 1996.

No context found.

Y. Bartal, A. Fiat, and S. Leonardi, Lower bounds for on-line graph problems with application to on-line circuit and optical routing, in Proceedings of the 28th Symposium Theory of Computing, 1996, pp. 531--540.

No context found.

Y. Bartal, A. Fiat, and S. Leonardi. Lower bounds for on-line graph problems with application to on-line circuit and optical routing. In Proceedings of the 28th ACM Symposium on Theory of Computing, pages 531--540, 1996.

No context found.

Yair Bartal, Amos Fiat, and Stefano Leonardi. Lower bounds for on-line graph problems with application to on-line circuit and optical routing. In Proc. 28th Symp. Theory of Computing, pages 531--540, 1996.

No context found.

Y. Bartal, A. Fiat and S. Leonardi, "Lower bounds for on-line graph problems with application to on-line circuit and optical routing", Proceedings of the 28-th Annual ACM Symposium on Theory of Computing (STOC 96), pp. 531-540, 1996.

....an O(log Delta) competitive algorithm for trees, where Delta is the diameter of the tree. They also show a matching lower bound. Kleinberg and Tardos [KT95] give O(log n) competitive algorithm for meshes (and some generalization) improving upon a previous result of [AGLR94] Bartal et al. BFL96] prove that for various routing problems including the throughput version of virtual circuit routing and the path coloring problem there exist networks where the competitive ratio is Omega Gamma n ffl ) for some fixed ffl) for any randomized algorithm. Finally, the on line version of ....

Y. Bartal, A. Fiat, S. Leonardi. Lower Bounds for On-line Graph Problems with Application to On-line Circuit and Optical Routing. Proc. of STOC'96.

....algorithm for trees, and an O( log log n) factor approximation algorithm for meshes. In the online setting, we give the first polylogarithmic competitive online algorithm for tree and mesh topologies. No polylogarithmic competitive algorithm is possible on general network topologies [BFL96] and there exists a polylogarithmic lower bound on the competitive ratio of any online algorithm on tree topologies [AAFL96] We prove the same lower bound for meshes. 1 Introduction Multicast routing and admission control are the basic operations required by future high speed communication ....

....to a O(log n) factor approximation for the escape problem for multicasts. We use instead a recursive approach that achieves a O( log log n) factor approximation. For the online problem no algorithm, not even a randomized one, has a polylogarithmic competitive ratio for any network topology [BFL96] for the unicast problem. Deterministic algorithms for the unicast problem have a very high lower bound even for line networks [AAP93] This clearly extends also to the multicast problem. Therefore in the unicast setting restricted graph topologies like trees, meshes, and densely embedded, ....

Y. Bartal, A. Fiat, and S. Leonardi. Lower bounds for on-line graph problems with application to on-line circuit and optical routing. In Proceedings of the 28th ACM Symposium on Theory of Computing, pages 531--540, 1996.

....Vishwanathan [Vis90] gives an O(n= log n) competitive randomized algorithm, improving over the O(n= log n) deterministic bound of Lov asz, Saks and Trotter [LST89] Halld orson and Szegedy [HS92] give an Omega (n= log n) randomized lower bound for the problem. Bartal Fiat and Leonardi [BFL96] study the model in which a graph G is known in advance to the online algorithm. The sequence oe may contain only a subset of the vertices of G. The algorithm must color the subgraph of G induced by the vertices of oe. The authors show that even under this model an Omega (n ffl ) randomized ....

....and the chromatic number of the interval graph, i.e. the maximum number of intervals overlapping at the same point of the line. A lower bound for randomized algorithms against an oblivious adversary is established using the application of Yao s Lemma [Yao77] to online algorithms [BEY98,BFL96] A lower bound over the competitive ratio of randomized algorithms is obtained proving a lower bound on the competitive ratio of deterministic online algorithms for a specific probability distribution over the input sequences for the problem. We first give some notation. We will denote by P ....

Y. Bartal, A. Fiat, and S. Leonardi. Lower bounds for on-line graph problems with application to on-line circuit and optical routing. In Proceedings of the 28th ACM Symposium on Theory of Computing, pages 531--540, 1996.

No context found.

Y. Bartal, A. Fiat, and S. Leonardi. Lower bounds for on-line graph problems with application to on-line circuit and optical routing. In Proceedings of the 28th Annual ACM Symposium on Theory of Computing, pages 531--540, 1996.

No context found.

Y. Bartal, A. Fiat, and S. Leonardi. Lower bounds for on-line graph problems with application to on-line circuit and optical routing. In Proc. of the 28th ACM Symposium on Theory of Computing, pages 531--540, 1996.

No context found.

Yair Bartal, Amos Fiat, and Stefano Leonardi. Lower bounds for on-line graph problems with application to on-line circuit and optical routing. In Proc. 28th Symp. Theory of Computing, pages 531--540, 1996.

No context found.

Y. Bartal, A. Fiat, and S. Leonardi. Lower bounds for on-line graph problems with application to on-line circuit and optical routing. In Proc. of the 28th ACM Symposium on Theory of Computing, pages 531--540, 1996.

No context found.

Y. Bartal, A. Fiat, and S. Leonardi. Lower bounds for on-line graph problems with application to on-line circuit and optical routing. In Proc. of the 28th ACM Symposium on Theory of Computing, pages 531-540, 1996.

No context found.

Y. Bartal, A. Fiat, and S. Leonardi. Lower Bounds for On--line Graph Problems with Applications to On--line Circuit and Optical Routing. In Proc. of the 28th Annual ACM Symposium on Theory of Computing (STOC '96), 1996.

No context found.

Y. Bartal, A. Fiat, S. Leonardi, "Lower bounds for on-line graph problems with application to on-line circuit and optical routing," Proc. 28th ACM Symp. on Theory of Computing, 1996.

No context found.

Y. Bartal, A. Fiat, and S. Leonardi. Lower bounds for on-line graph problems with application to on-line circuit and optical routing. In Proc. of the 28th ACM Symposium on Theory of Computing, pages 531--540, 1996.

No context found.

Y. Bartal, A. Fiat, and S. Leonardi. Lower bounds for on-line graph problems with application to on-line circuit and optical routing. In Proc. of the 28th ACM Symposium on Theory of Computing, pages 531-540, 1996.

No context found.

Y. Bartal, A. Fiat, and S. Leonardi. Lower Bounds for On--line Graph Problems with Applications to On--line Circuit and Optical Routing. In Proc. of the 28th Annual ACM Symposium on Theory of Computing (STOC '96), 1996.

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