000			03977nam a22005295i 4500
001			978-3-642-22015-9
003			DE-He213
005			20140220083258.0
007			cr nn 008mamaa
008			120109s2012 gw | s |||| 0|eng d
020			_a9783642220159 _9978-3-642-22015-9
024	7		_a10.1007/978-3-642-22015-9 _2doi
050		4	_aT57-57.97
072		7	_aPBW _2bicssc
072		7	_aMAT003000 _2bisacsh
082	0	4	_a519 _223
100	1		_aGärtner, Bernd. _eauthor.
245	1	0	_aApproximation Algorithms and Semidefinite Programming _h[electronic resource] / _cby Bernd Gärtner, Jiri Matousek.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2012.
300			_aXI, 251p. 23 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0		_aPart I (by Bernd Gärtner): 1 Introduction: MAXCUT via Semidefinite Programming -- 2 Semidefinite Programming -- 3 Shannon Capacity and Lovász Theta.-  4 Duality and Cone Programming.-  5 Approximately Solving Semidefinite Programs -- 6 An Interior-Point Algorithm for Semidefinite Programming -- 7 Compositive Programming.-  Part II (by Jiri Matousek): 8 Lower Bounds for the Goemans–Williamson MAXCUT Algorithm -- 9 Coloring 3-Chromatic Graphs -- 10 Maximizing a Quadratic Form on a Graph -- 11 Colorings With Low Discrepancy -- 12 Constraint Satisfaction Problems, and Relaxing Them Semidefinitely -- 13 Rounding Via Miniatures -- Summary -- References -- Index.
520			_aSemidefinite programs constitute one of the largest classes of optimization problems that can be solved with reasonable efficiency - both in theory and practice. They play a key role in a variety of research areas, such as combinatorial optimization, approximation algorithms, computational complexity, graph theory, geometry, real algebraic geometry and quantum computing. This book is an introduction to selected aspects of semidefinite programming and its use in approximation algorithms. It covers the basics but also a significant amount of recent and more advanced material.   There are many computational problems, such as MAXCUT, for which one cannot reasonably expect to obtain an exact solution efficiently, and in such case, one has to settle for approximate solutions. For MAXCUT and its relatives, exciting recent results suggest that semidefinite programming is probably the ultimate tool. Indeed, assuming the Unique Games Conjecture, a plausible but as yet unproven hypothesis, it was shown that for these problems, known algorithms based on semidefinite programming deliver the best possible approximation ratios among all polynomial-time algorithms.   This book follows the “semidefinite side” of these developments, presenting some of the main ideas behind approximation algorithms based on semidefinite programming. It develops the basic theory of semidefinite programming, presents one of the known efficient algorithms in detail, and describes the principles of some others. It also includes applications, focusing on approximation algorithms.
650		0	_aMathematics.
650		0	_aInformation theory.
650		0	_aComputer software.
650		0	_aComputational complexity.
650		0	_aAlgorithms.
650		0	_aMathematical optimization.
650	1	4	_aMathematics.
650	2	4	_aApplications of Mathematics.
650	2	4	_aTheory of Computation.
650	2	4	_aAlgorithm Analysis and Problem Complexity.
650	2	4	_aDiscrete Mathematics in Computer Science.
650	2	4	_aAlgorithms.
650	2	4	_aOptimization.
700	1		_aMatousek, Jiri. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783642220142
856	4	0	_uhttp://dx.doi.org/10.1007/978-3-642-22015-9
912			_aZDB-2-SMA
999			_c102017 _d102017