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Can one find External Source Input Expressions for which there exist Map Reduce Configurations?

Ravi (Ravinder), Kiran M.
<span title="2015-10-15">2015</span> <i title="Foundation of Computer Science"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/b637noqf3vhmhjevdfk3h5pdsu" style="color: black;">International Journal of Computer Applications</a> </i> &nbsp;
This instruction concept will be referred to as approximation set instruction (ASI) since the weights are concentrated on approximate minimizers of the optimization problem.  ...  This process defines the approximation problem R(s, ) = 1 2 (ns • ) on the reducer side.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5120/ijca2015906680">doi:10.5120/ijca2015906680</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ikghlleiczhojh6rxlx6vyw6ym">fatcat:ikghlleiczhojh6rxlx6vyw6ym</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180604023139/https://www.ijcaonline.org/research/volume128/number12/g-2015-ijca-906680.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/88/70/8870eb7a519f3558e2d7339d71139c05bef6009c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5120/ijca2015906680"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Minimizing NFA's and Regular Expressions [chapter]

Gregor Gramlich, Georg Schnitger
<span title="">2005</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;
Our inapproximability results for a given dfa with n states are based on cryptographic assumptions and we show that any efficient algorithm will have an approximation factor of at least n poly(log n) .  ...  Our setup also allows us to analyze the minimum consistent dfa problem.  ...  Assumption: N P ⊆ DT IM E(n O(log n) ) Good News: Cyclic case can be approximated within 1 + ln k. Reference: [6] , [3]  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-31856-9_33">doi:10.1007/978-3-540-31856-9_33</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/62akhfsipfc4vnp4t7skenc64e">fatcat:62akhfsipfc4vnp4t7skenc64e</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170810222304/http://ggramlich.github.io/Publications/approximationSTACS05.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/cb/94/cb9486498319bae7bf0d28e5960115e2571bf2f2.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-31856-9_33"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

New hardness results for congestion minimization and machine scheduling

Julia Chuzhoy, Joseph (Seffi) Naor
<span title="">2004</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jlc5kugafjg4dl7ozagimqfcbm" style="color: black;">Proceedings of the thirty-sixth annual ACM symposium on Theory of computing - STOC &#39;04</a> </i> &nbsp;
Both problems are known to be O(log n/ log log n)-approximable via the randomized rounding technique of Raghavan and Thompson.  ...  We study the approximability of two natural NP-hard problems. The first problem is congestion minimization in directed networks.  ...  Our Results We prove hardness of approximation for congestion minimization in directed networks and for the machine minimization problem with discrete input.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1007352.1007364">doi:10.1145/1007352.1007364</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/stoc/ChuzhoyN04.html">dblp:conf/stoc/ChuzhoyN04</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/j3hfmjm2wncg5lhm4uwbrvecje">fatcat:j3hfmjm2wncg5lhm4uwbrvecje</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20081002131556/http://ttic.uchicago.edu/~cjulia/papers/congestion-journal.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/dd/27/dd27cffdfbb658f55dd9d9159b96de55b5bd1ed5.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1007352.1007364"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Tighter Low-rank Approximation via Sampling the Leveraged Element [chapter]

Srinadh Bhojanapalli, Prateek Jain, Sujay Sanghavi
<span title="2014-12-22">2014</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-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms</a> </i> &nbsp;
executes weighted alternating minimization (as before) on these.  ...  In this work, we propose a new randomized algorithm for computing a low-rank approximation to a given matrix.  ...  In this model, one is interested in find good approximations while minimizing both computations and the communication burden on the center.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/1.9781611973730.62">doi:10.1137/1.9781611973730.62</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/soda/Bhojanapalli0S15.html">dblp:conf/soda/Bhojanapalli0S15</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/uddz5bu33nbd5ju66vgazenas4">fatcat:uddz5bu33nbd5ju66vgazenas4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20150927041114/http://stanford.edu/~rezab/nips2014workshop/submits/tight.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/c6/38/c638d0023a449b3631b2f01ce2efbe21d572e355.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/1.9781611973730.62"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Bounded Degree Group Steiner Tree Problems [chapter]

Guy Kortsarz, Zeev Nutov
<span title="">2020</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Our first result generalizes [10]we give a bicriteria (O(log 2 n), O(log 2 n))-approximation algorithm for Degrees Bounded Min-Cost Group Steiner Tree problem on tree inputs.  ...  When the input is a tree, an O(log 2 n) approximation for the cost is given in [10] .  ...  Bounded Degrees Min-Cost Group Steiner Tree on tree inputs admits a bicriteria randomized (O(log 2 n), O(log 2 n))-approximation algorithm.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-030-48966-3_26">doi:10.1007/978-3-030-48966-3_26</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/t3u7nfs7n5edfcze4mm5p4g7ju">fatcat:t3u7nfs7n5edfcze4mm5p4g7ju</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20201108033447/https://link.springer.com/content/pdf/10.1007%2F978-3-030-48966-3_26.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/2c/66/2c66d457b256f81a8b2fbf350553ad3aa4cc82d1.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-030-48966-3_26"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Private Approximation of Search Problems

Amos Beimel, Paz Carmi, Kobbi Nissim, Enav Weinreb
<span title="">2009</span> <i title="Society for Industrial &amp; Applied Mathematics (SIAM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/7dys7zoberdktmxyjciuy5bnse" style="color: black;">SIAM journal on computing (Print)</a> </i> &nbsp;
Although our privacy requirement seems minimal, we show that for well studied problems, as vertex cover and maximum exact 3SAT, private approximation algorithms are unlikely to exist even for poor approximation  ...  Generalizing this requirement to search problems is not straight forward as an input may have many different outputs.  ...  If RP = N P, then there is no randomized n 1− -approximation algorithm for the search problem of minVC that leaks at most 8 log n bits.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/060671899">doi:10.1137/060671899</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jkux3a6eqjdatcjz7mdv4v3uzy">fatcat:jkux3a6eqjdatcjz7mdv4v3uzy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170706075505/https://eccc.weizmann.ac.il/report/2005/141/download/" 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/4e/2f/4e2ff8754a08bcc555dfdd289ae529037c0d9461.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/060671899"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Private approximation of search problems

Amos Beimel, Paz Carmi, Kobbi Nissim, Enav Weinreb
<span title="">2006</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jlc5kugafjg4dl7ozagimqfcbm" style="color: black;">Proceedings of the thirty-eighth annual ACM symposium on Theory of computing - STOC &#39;06</a> </i> &nbsp;
Although our privacy requirement seems minimal, we show that for well studied problems, as vertex cover and maximum exact 3SAT, private approximation algorithms are unlikely to exist even for poor approximation  ...  Generalizing this requirement to search problems is not straight forward as an input may have many different outputs.  ...  If RP = N P, then there is no randomized n 1− -approximation algorithm for the search problem of minVC that leaks at most 8 log n bits.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1132516.1132533">doi:10.1145/1132516.1132533</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/stoc/BeimelCNW06.html">dblp:conf/stoc/BeimelCNW06</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fvjkh5hudbhf7nnersmatgv75i">fatcat:fvjkh5hudbhf7nnersmatgv75i</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170706075505/https://eccc.weizmann.ac.il/report/2005/141/download/" 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/4e/2f/4e2ff8754a08bcc555dfdd289ae529037c0d9461.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1132516.1132533"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Minimizing nfa's and regular expressions

Gregor Gramlich, Georg Schnitger
<span title="">2007</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p6ovb2qpkfenhmb7mcksobrcxq" style="color: black;">Journal of computer and system sciences (Print)</a> </i> &nbsp;
Our inapproximability results for a given dfa with n states are based on cryptographic assumptions and we show that any efficient algorithm will have an approximation factor of at least n poly(log n) .  ...  Our setup also allows us to analyze the minimum consistent dfa problem.  ...  REMARK: Cyclic case can be approximated within 1 + ln k. REFERENCE: [7] , [3] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jcss.2006.11.002">doi:10.1016/j.jcss.2006.11.002</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qjmbv4bd2nhezanp4o4l2tjjxi">fatcat:qjmbv4bd2nhezanp4o4l2tjjxi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190414001243/https://core.ac.uk/download/pdf/82240385.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/bc/f7/bcf74676fd40d4b6ad59fa9a372100a3d449bae8.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jcss.2006.11.002"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Tight results for clustering and summarizing data streams

Sudipto Guha
<span title="">2009</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/rw5iczhdevgrhi35u5qetcouce" style="color: black;">Proceedings of the 12th International Conference on Database Theory - ICDT &#39;09</a> </i> &nbsp;
We provide a simple framework that improves upon all previous algorithms on these problems in either the space bound, the approximation factor or the running time.  ...  This property of accurate estimation is true of all known upper bounds on these problems.  ...  To see the time bound, consider, instead of running the thresholded algorithm on one input, to batch t = O( B log 1 ) inputs.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1514894.1514926">doi:10.1145/1514894.1514926</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/icdt/Guha09.html">dblp:conf/icdt/Guha09</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nr4y47pxcfawffacroq5gngija">fatcat:nr4y47pxcfawffacroq5gngija</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20090115215658/http://www.cis.upenn.edu/~sudipto/mypapers/kcen.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/56/c8/56c865b6de96b682a1279462bf21c266f4600a23.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1514894.1514926"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Approximation and Streaming Algorithms for Projective Clustering via Random Projections [article]

Michael Kerber, Sharath Raghvendra
<span title="2015-06-02">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Using this dimension reduction result, we obtain new approximation and streaming algorithms for projective clustering problems.  ...  In the projective clustering problem, given k, q and norm ρ∈ [1,∞], we have to compute a set F of k q-dimensional flats such that (∑_p∈ Pd(p, F)^ρ)^1/ρ is minimized; here d(p, F) represents the (Euclidean  ...  The early algorithms for these problems had exponential dependence on d [2, 4] and were well-suited for low-dimensional inputs.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1407.2063v2">arXiv:1407.2063v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pp4g57hynzgwdekplkvzboyova">fatcat:pp4g57hynzgwdekplkvzboyova</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200826204216/https://arxiv.org/pdf/1407.2063v2.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/62/16/6216f2df8c12bb15d0a6ca48e32a5c23d3d11cca.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1407.2063v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Bounded Degree Group Steiner Tree Problems [article]

Guy Kortsarz, Zeev Nutov
<span title="2019-10-28">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We give a bicriteria (O(log N log | S|),O(log^2 n))-approximation algorithm for this problem on tree inputs, where N is the size of the largest group, generalizing the approximation of Garg, Konjevod,  ...  We show that if the former problem admits approximation ratio ρ then the later problem admits approximation ratio ρ· O(log k).  ...  We got that with probability 1 − 1/n 2 , for a given v, deg(v) = O(log 2 n) · b v . By the union bound with probability 1 − 1/n for every v, deg(v) ≤ O(log 2 n) · b v .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1910.12848v1">arXiv:1910.12848v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wa4zb4jmqbcs7nsbk3gg3ll26y">fatcat:wa4zb4jmqbcs7nsbk3gg3ll26y</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200915034317/https://arxiv.org/pdf/1910.12848v1.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/19/83/19832bd66d948b9a04ed8589767c97b6df126fdf.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1910.12848v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Improved distributed steiner forest construction

Christoph Lenzen, Boaz Patt-Shamir
<span title="">2014</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/t5fzg7fyy5byfdcl2vrzbn43ty" style="color: black;">Proceedings of the 2014 ACM symposium on Principles of distributed computing - PODC &#39;14</a> </i> &nbsp;
We also prove a matching lower bound ofΩ(k + min {s, √ n} + D) on the running time of any distributed approximation algorithm for the Steiner Forest problem.  ...  Previous algorithms were randomized, and obtained either an O(log n)-approximation inÕ(sk) time, or an O(1/ε)-approximation inÕ(( √ n + t) 1+ε + D) time.  ...  [16] , where a randomized algorithm is used to embed the instance in a virtual tree with O(log n) distortion, then finding the optimal solution on the tree (which is just the minimal subforest connecting  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2611462.2611464">doi:10.1145/2611462.2611464</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/podc/LenzenP14.html">dblp:conf/podc/LenzenP14</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fi6l7yjw6zduveiwpcfdt3hp24">fatcat:fi6l7yjw6zduveiwpcfdt3hp24</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20151022153007/http://groups.csail.mit.edu/tds/papers/Lenzen/PODC14.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/99/9b/999b21871a798bc21fb2bb86337e5db6d30a9d11.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2611462.2611464"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Flows on Few Paths: Algorithms and Lower Bounds [chapter]

Maren Martens, Martin Skutella
<span title="">2004</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;
We prove a lower bound of Ω(log m/ log log m) on the performance of a general class of algorithms for minimizing congestion where m is the number of edges in a graph.  ...  We present approximation results for two versions of this problem with the objective to minimize the congestion of the network.  ...  Raghavan and Thompson [20, 19] introduce a randomized rounding technique which gives an O(log m/ log log m)-approximation algorithm for the problem of minimizing congestion for the UFP if the maximum  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-30140-0_47">doi:10.1007/978-3-540-30140-0_47</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7u6c6d7q2vgxxf2owbgp56v7pa">fatcat:7u6c6d7q2vgxxf2owbgp56v7pa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20081031205350/http://www.math.tu-berlin.de/~skutella/few-paths.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/e8/c0/e8c0bee60793a4e9c9c833a007b1ac33e972dc18.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-30140-0_47"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Flows on few paths: Algorithms and lower bounds

Maren Martens, Martin Skutella
<span title="">2006</span> <i title="Wiley"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p4qgtym3grdnngfxilwqjjxqy4" style="color: black;">Networks</a> </i> &nbsp;
We prove a lower bound of Ω(log m/ log log m) on the performance of a general class of algorithms for minimizing congestion where m is the number of edges in a graph.  ...  We present approximation results for two versions of this problem with the objective to minimize the congestion of the network.  ...  Raghavan and Thompson [20, 19] introduce a randomized rounding technique which gives an O(log m/ log log m)-approximation algorithm for the problem of minimizing congestion for the UFP if the maximum  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1002/net.20121">doi:10.1002/net.20121</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/udv6w35qsvdslhzur56grr6wpm">fatcat:udv6w35qsvdslhzur56grr6wpm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20081031205350/http://www.math.tu-berlin.de/~skutella/few-paths.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/e8/c0/e8c0bee60793a4e9c9c833a007b1ac33e972dc18.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1002/net.20121"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> wiley.com </button> </a>

On the Probe Complexity of Local Computation Algorithms

Uriel Feige, Boaz Patt-Shamir, Shai Vardi, Michael Wagner
<span title="2018-06-29">2018</span> <i > <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/pf6v2q6ji5h7birkbrtpdc2uhy" style="color: black;">International Colloquium on Automata, Languages and Programming</a> </i> &nbsp;
We show that there are problems that have very efficient LCAs on any graph -specifically, we show that there is an LCA for the weak coloring problem (where a coloring is legal if every vertex has a neighbor  ...  For strong probes, our negative result for maximal matching is complemented by an LCA for (1 − )-approximate maximum matching on regular graphs that uses O(1) strong probes, for any constant > 0.  ...  In this work, except where explicitly mentioned, we allow the random seed to be unbounded. 5 The definition of approximation algorithms to minimization problems is analogous, with α ≥ 1.I C A L P 2 0  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.icalp.2018.50">doi:10.4230/lipics.icalp.2018.50</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/icalp/FeigePV18.html">dblp:conf/icalp/FeigePV18</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/uhuf7wp4jrh6jccxrb4iymfwzi">fatcat:uhuf7wp4jrh6jccxrb4iymfwzi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220130051624/https://drops.dagstuhl.de/opus/volltexte/2018/9054/pdf/LIPIcs-ICALP-2018-50.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/45/33/4533503066351c31e5f1f05e29cc22a612c1a4c1.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.icalp.2018.50"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>
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