Faster Algorithms for MAX CUT and MAX CSP, with Polynomial Expected Time for Sparse Instances
We show that a random instance of a weighted maximum constraint satisfaction problem (or max 2-csp), whose clauses are over pairs of binary variables, is solvable by a deterministic algorithm in polynomial expected time, in the “sparse” regime where the expected number of clauses is half the number...
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| creator | Scott, Alexander D. Sorkin, Gregory B. |
| description | We show that a random instance of a weighted maximum constraint satisfaction problem (or max 2-csp), whose clauses are over pairs of binary variables, is solvable by a deterministic algorithm in polynomial expected time, in the “sparse” regime where the expected number of clauses is half the number of variables. In particular, a maximum cut in a random graph with edge density 1/n or less can be found in polynomial expected time.
Our method is to show, first, that if a max 2-csp has a connected underlying graph with n vertices and m edges, the solution time can be deterministically bounded by 2(m − n)/2. Then, analyzing the tails of the distribution of this quantity for a component of a random graph yields our result. An alternative deterministic bound on the solution time, as 2m/5, improves upon a series of recent results. |
| doi_str_mv | 10.1007/978-3-540-45198-3_32 |
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Our method is to show, first, that if a max 2-csp has a connected underlying graph with n vertices and m edges, the solution time can be deterministically bounded by 2(m − n)/2. Then, analyzing the tails of the distribution of this quantity for a component of a random graph yields our result. An alternative deterministic bound on the solution time, as 2m/5, improves upon a series of recent results.</description><identifier>ISSN: 0302-9743</identifier><identifier>ISBN: 9783540407706</identifier><identifier>ISBN: 3540407707</identifier><identifier>EISSN: 1611-3349</identifier><identifier>EISBN: 9783540451983</identifier><identifier>EISBN: 3540451986</identifier><identifier>DOI: 10.1007/978-3-540-45198-3_32</identifier><identifier>OCLC: 957125146</identifier><identifier>LCCallNum: QA76.758</identifier><language>eng</language><publisher>Germany: Springer Berlin / Heidelberg</publisher><subject>Algorithms & data structures ; Applied sciences ; Artificial intelligence ; Computer science; control theory; systems ; Cyclomatic Number ; Dense Instance ; Discrete mathematics ; Exact sciences and technology ; Mathematical theory of computation ; Pattern recognition. Digital image processing. Computational geometry ; Random Graph ; Software ; Sparse Random Graph ; Speech and sound recognition and synthesis. Linguistics ; Underlying Graph</subject><ispartof>Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, 2003, Vol.2764, p.382-395</ispartof><rights>Springer-Verlag Berlin Heidelberg 2003</rights><rights>2004 INIST-CNRS</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c369t-c27391f7ce74d396e235488a33c99314732bfdb329d385d5550be091c5b4e7c63</citedby><relation>Lecture Notes in Computer Science</relation></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Uhttps://ebookcentral.proquest.com/covers/4516828-l.jpg</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/978-3-540-45198-3_32$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/978-3-540-45198-3_32$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>309,310,777,778,782,787,788,791,4038,4039,27914,38244,41431,42500</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=15692310$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><contributor>Jansen, Klaus</contributor><contributor>Arora, Sanjeev</contributor><contributor>Rolim, Jose D. P</contributor><contributor>Sahai, Amit</contributor><contributor>Sahai, Amit</contributor><contributor>Arora, Sanjeev</contributor><contributor>Jansen, Klaus</contributor><contributor>Rolim, José D. P.</contributor><creatorcontrib>Scott, Alexander D.</creatorcontrib><creatorcontrib>Sorkin, Gregory B.</creatorcontrib><title>Faster Algorithms for MAX CUT and MAX CSP, with Polynomial Expected Time for Sparse Instances</title><title>Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques</title><description>We show that a random instance of a weighted maximum constraint satisfaction problem (or max 2-csp), whose clauses are over pairs of binary variables, is solvable by a deterministic algorithm in polynomial expected time, in the “sparse” regime where the expected number of clauses is half the number of variables. In particular, a maximum cut in a random graph with edge density 1/n or less can be found in polynomial expected time.
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Our method is to show, first, that if a max 2-csp has a connected underlying graph with n vertices and m edges, the solution time can be deterministically bounded by 2(m − n)/2. Then, analyzing the tails of the distribution of this quantity for a component of a random graph yields our result. An alternative deterministic bound on the solution time, as 2m/5, improves upon a series of recent results.</abstract><cop>Germany</cop><pub>Springer Berlin / Heidelberg</pub><doi>10.1007/978-3-540-45198-3_32</doi><oclcid>957125146</oclcid><tpages>14</tpages><oa>free_for_read</oa></addata></record> |
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| identifier | ISSN: 0302-9743 |
| ispartof | Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, 2003, Vol.2764, p.382-395 |
| issn | 0302-9743 1611-3349 |
| language | eng |
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| source | Springer Books |
| subjects | Algorithms & data structures Applied sciences Artificial intelligence Computer science control theory systems Cyclomatic Number Dense Instance Discrete mathematics Exact sciences and technology Mathematical theory of computation Pattern recognition. Digital image processing. Computational geometry Random Graph Software Sparse Random Graph Speech and sound recognition and synthesis. Linguistics Underlying Graph |
| title | Faster Algorithms for MAX CUT and MAX CSP, with Polynomial Expected Time for Sparse Instances |
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