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Randomized algorithm for the k-server problem on decomposable spaces [article]

Judit Nagy-György
<span title="2007-08-17">2007</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We study the randomized k-server problem on metric spaces consisting of widely separated subspaces.  ...  This method yields o(k)-competitive algorithms solving the randomized k-server problem, for some special underlying metric spaces, e.g. HSTs of "small" height (but unbounded degree).  ...  Ø Ø Ö Ü ×Ø× Ö Ò ÓÑ Þ Ð ÓÖ Ø Ñ Û Ø ÓÑÔ Ø ¹ Ø Ú Ö Ø Ó Θ(log k) Ò ÒÝ Ñ ØÖ ×Ô º Ì ×Ø ÒÓÛÒ ÐÓÛ Ö ÓÙÒ × Ω(log k/ log 2 log k) ¿℄º Ò ØÙÖ Ð ÙÔÔ Ö ÓÙÒ × Ø ÓÙÒ 2k + 1 Ú Ò ÓÖ Ø Ø ÖÑ Ò ×Ø × º Ý Ö ¹ ×ØÖ Ø Ò ÓÙÖ ØØ  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0708.2351v1">arXiv:0708.2351v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dbrtrzsfffhvxh5qzlirzwvtoq">fatcat:dbrtrzsfffhvxh5qzlirzwvtoq</a> </span>
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Randomized algorithm for the k-server problem on decomposable spaces

Judit Nagy-György
<span title="">2009</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/usw2n4yaarcurchx7i4on2iqea" style="color: black;">Journal of Discrete Algorithms</a> </i> &nbsp;
We study the randomized k-server problem on metric spaces consisting of widely separated subspaces.  ...  This method yields o(k)-competitive algorithms solving the randomized k-server problem for some special underlying metric spaces, e.g. HSTs of "small" height (but unbounded degree).  ...  Observe that if A is (f, µ)-efficient on N , then A is f (k)-competitive for the k-server problem on N for any 0 < k < µ.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jda.2009.02.005">doi:10.1016/j.jda.2009.02.005</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/d3267f4pcnd4le5rgtlt54cjlu">fatcat:d3267f4pcnd4le5rgtlt54cjlu</a> </span>
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Randomized k-server algorithms for growth-rate bounded graphs

Yair Bartal, Manor Mendel
<span title="">2005</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/anp7kqfyerdljfxydqb4objj6a" style="color: black;">Journal of Algorithms</a> </i> &nbsp;
The paper referred to in the title is withdrawn.  ...  An Algorithm for Decomposable Spaces We recall some concepts from the servers problem on uniform spaces (also known as the paging problem).  ...  If M is α-probabilistically approximated by S and for each S ∈ S there is r-competitive randomized k-server algorithm, then M has αr competitive randomized algorithm for the k-server problem.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jalgor.2004.06.002">doi:10.1016/j.jalgor.2004.06.002</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lutklkxed5dcdc7og6r6umpohu">fatcat:lutklkxed5dcdc7og6r6umpohu</a> </span>
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A General Decomposition Theorem for the k-Server Problem

Steven S. Seiden
<span title="">2002</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/joe2ngto45hbnl3pncnesnq344" style="color: black;">Information and Computation</a> </i> &nbsp;
The first general decomposition theorem for the k-server problem is presented.  ...  The only other cases for which polylogarithmic competitive randomized algorithms are known are the uniform metric space, and the weighted cache metric space with two weights.  ...  A k-Server Algorithm for Decomposable Spaces We now develop an algorithm for any metric space that is θ-decomposable.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1006/inco.2002.3144">doi:10.1006/inco.2002.3144</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zidg5lo5mvb2hony424mevhyia">fatcat:zidg5lo5mvb2hony424mevhyia</a> </span>
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A General Decomposition Theorem for the k-Server Problem [chapter]

Steven S. Seiden
<span title="">2001</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
The first general decomposition theorem for the k-server problem is presented.  ...  This theorem implies O(polylog(k))-competitive algorithms for certain metric spaces consisting of a polylogarithmic number of widely separated sub-spaces.  ...  A k-Server Algorithm for Decomposable Spaces We now develop an algorithm for any metric space that is θ-decomposable.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-44676-1_7">doi:10.1007/3-540-44676-1_7</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6kkuvndsgnak3e6ccrtmfvmxlq">fatcat:6kkuvndsgnak3e6ccrtmfvmxlq</a> </span>
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R–LINE: A better randomized 2-server algorithm on the line

Lucas Bang, Wolfgang Bein, Lawrence L. Larmore
<span title="">2015</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
A randomized on-line algorithm is given for the 2-server problem on the line, with competitiveness less than 1.901 against the oblivious adversary.  ...  This improves the previously best known competitiveness of 155 78 ≈ 1.987 for the problem. The algorithm uses a new approach and defines a potential in terms of isolation indices from T-theory.  ...  Acknowledgement Part of the work of author Wolfgang Bein was supported by National Science Foundation grant IIA 1427584.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.tcs.2015.08.043">doi:10.1016/j.tcs.2015.08.043</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/uyn2nh2id5cevdin5sqlugrpou">fatcat:uyn2nh2id5cevdin5sqlugrpou</a> </span>
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R–LINE: A Better Randomized 2-Server Algorithm on the Line [chapter]

Lucas Bang, Wolfgang Bein, Lawrence L. Larmore
<span title="">2013</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
A randomized on-line algorithm is given for the 2-server problem on the line, with competitiveness less than 1.901 against the oblivious adversary.  ...  This improves the previously best known competitiveness of 155 78 ≈ 1.987 for the problem. The algorithm uses a new approach and defines a potential in terms of isolation indices from T-theory.  ...  Acknowledgement Part of the work of author Wolfgang Bein was supported by National Science Foundation grant IIA 1427584.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-38016-7_11">doi:10.1007/978-3-642-38016-7_11</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mllli7t52fdrrnjwk3xfxady4i">fatcat:mllli7t52fdrrnjwk3xfxady4i</a> </span>
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Page 1283 of Mathematical Reviews Vol. , Issue 2001B [page]

<span title="">2001</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
algorithm for two servers on the line.  ...  This implies that one unbiased random bit is not sufficient to improve the ratio of 2 for the two-server problem.  ... 
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On the Cryptographic Complexity of the Worst Functions [chapter]

Amos Beimel, Yuval Ishai, Ranjit Kumaresan, Eyal Kushilevitz
<span title="">2014</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
The worst-case complexity of the best previous solutions was Ω(N ) for the first three problems and Ω(N/ log N ) for the last one.  ...  For every graph G on N nodes, there is a secret-sharing scheme for N parties in which each pair of parties can reconstruct the secret if and only if the corresponding nodes in G are connected, and where  ...  A k-server decomposable PIR protocol P = (Q, A, R) for F N,k−1 consists of three algorithms: a randomized query algorithm Q, an answering algorithm A, and a reconstruction algorithm R.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-54242-8_14">doi:10.1007/978-3-642-54242-8_14</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/q3ccfhvn5jea5fnlvvqoydjhau">fatcat:q3ccfhvn5jea5fnlvvqoydjhau</a> </span>
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A Novel Algorithm of Quantum Random Walk in Server Traffic Control and Task Scheduling

Dong Yumin, Xiao Shufen
<span title="">2014</span> <i title="Hindawi Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/xdzjuti5nzejrghubfpezefpqi" style="color: black;">Journal of Applied Mathematics</a> </i> &nbsp;
For the data clustering problem of high dimensional space, we can decompose onem-dimensional quantum random walk intomone-dimensional quantum random walk.  ...  We introduce the method of random walk and illuminate what the quantum random walk is. Here, we mainly research the standard model of one-dimensional quantum random walk.  ...  Acknowledgment This work is supported by the National Natural Science Foundation of China (61173056).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2014/818479">doi:10.1155/2014/818479</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jzgz62izkfbftgi3powk3a34tu">fatcat:jzgz62izkfbftgi3powk3a34tu</a> </span>
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Intelligent resource allocation in mobile blockchain for privacy and security transactions: a deep reinforcement learning based approach

Zhaolong Ning, Shouming Sun, Xiaojie Wang, Lei Guo, Guoyin Wang, Xinbo Gao, Ricky Y. K. Kwok
<span title="2021-04-25">2021</span> <i title="Springer Science and Business Media LLC"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ikvx2lmj7rew7jpw4lygqgjpby" style="color: black;">Science China Information Sciences</a> </i> &nbsp;
We decompose the formulated problem into two subproblems to decrease the dimension of action space.  ...  Then, we propose a deep reinforcement learning additional particle swarm optimization (DRPO) algorithm to solve the two subproblems, in which a particle swarm optimization algorithm is leveraged to avoid  ...  In DRPO, we decompose the formulated problem into two subproblems to reduce the dimension of the action space, and PSO scheme is integrated to avoid the unnecessary random search for actions in DDPG.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s11432-020-3125-y">doi:10.1007/s11432-020-3125-y</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/djs7vowuzrezro6xhk33lfhfle">fatcat:djs7vowuzrezro6xhk33lfhfle</a> </span>
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Competitive Algorithms for Generalized k-Server in Uniform Metrics [article]

Nikhil Bansal, Marek Elias, Grigorios Koumoutsos, Jesper Nederlof
<span title="2017-07-17">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The generalized k-server problem is a far-reaching extension of the k-server problem with several applications. Here, each server s_i lies in its own metric space M_i.  ...  Despite much work, no f(k)-competitive algorithm is known for the problem for k > 2 servers, even for special cases such as uniform metrics and lines.  ...  Acknowledgments We would like to thank René Sitters for useful discussions on the generalized k-server problem.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1707.04519v2">arXiv:1707.04519v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7m3uplulvff33hj5mppbmbaaea">fatcat:7m3uplulvff33hj5mppbmbaaea</a> </span>
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Competitive Algorithms for Generalized k-Server in Uniform Metrics [chapter]

Nikhil Bansa, Marek Eliáš, Grigorios Koumoutsos, Jesper Nederlof
<span title="">2018</span> <i title="Society for Industrial and Applied Mathematics"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ja7dpjgz2nhjlovlil3ij5m7ei" style="color: black;">Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms</a> </i> &nbsp;
The generalized k-server problem is a far-reaching extension of the k-server problem with several applications. Here, each server s i lies in its own metric space M i .  ...  Despite much work, no f (k)-competitive algorithm is known for the problem for k > 2 servers, even for special cases such as uniform metrics and lines.  ...  Acknowledgments We would like to thank René Sitters for useful discussions on the generalized k-server problem.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/1.9781611975031.64">doi:10.1137/1.9781611975031.64</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/soda/Bansal0KN18.html">dblp:conf/soda/Bansal0KN18</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xohqzeopincunoilmeyv3ogoia">fatcat:xohqzeopincunoilmeyv3ogoia</a> </span>
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Distance Computation Between Binary Code and Real Vector for Efficient Keypoint Matching

Yuji Yamauchi, Mitsuru Ambai, Ikuro Sato, Yuichi Yoshida, Hironobu Fujiyoshi
<span title="">2013</span> <i title="Information Processing Society of Japan"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/tgkeoqpazzdvvd3eofpe7sjgwa" style="color: black;">IPSJ Transactions on Computer Vision and Applications</a> </i> &nbsp;
For second problem, we compute efficiently the Euclidean distance by decomposing the real vector into weight factors and binary basis vectors.  ...  Image recognition in client server system has a problem of data traffic. However, reducing data traffic gives rise to worsening of performance.  ...  [8] proposed decomposing the real vector y α into k weight factors and k binary basis vectors as y α ≈ Mc, (3) where c = (c 1 , c 2 , · · · , c k ) T ∈ R k is the weight factor and M = {m 1 , m 2 ,  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2197/ipsjtcva.5.124">doi:10.2197/ipsjtcva.5.124</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/773yp3youbby7kajiwn6sgqk2a">fatcat:773yp3youbby7kajiwn6sgqk2a</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809130254/http://vision.cs.chubu.ac.jp/mprg/c_group/c055_yamauchi2013.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/21/37/213778ab0c7097cbcb2b97257bca0f1a76ab21b5.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2197/ipsjtcva.5.124"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Randomized Algorithms for Dynamic Storage Load-Balancing

Liang Liu, Lance Fortnow, Jin Li, Yating Wang, Jun Xu
<span title="">2016</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/eitdfnn7k5fohgz7jhhim3f4bm" style="color: black;">Proceedings of the Seventh ACM Symposium on Cloud Computing - SoCC &#39;16</a> </i> &nbsp;
We propose a randomized algorithm, in which each dispatcher independently samples a blocks-to-disks assignment according to a probability distribution on a set of assignments conforming to the aforementioned  ...  In this work, we study a challenging research problem that arises in minimizing the cost of storing customer data online for reliable access in a cloud.  ...  Acknowledgments We thank anonymous reviewers for their insightful comments and suggestions that help improve the quality of the paper. We also thank Mr. Jian Huang and Prof.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2987550.2987572">doi:10.1145/2987550.2987572</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/cloud/LiuFLWX16.html">dblp:conf/cloud/LiuFLWX16</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nrevsox3bfaplpw44fj5c4cwra">fatcat:nrevsox3bfaplpw44fj5c4cwra</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190514065822/https://www.cc.gatech.edu/~jx/reprints/Liu%20et%20al.%20-%202016%20-%20Randomized%20Algorithms%20for%20Dynamic%20Storage%20Load-Bal.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/47/0d/470deaedd0fbc8b23a4605f5209e40f4b968d184.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2987550.2987572"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>
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