Fundamentals of parameterized complexity:
This comprehensive and self-contained textbook presents an accessible overview of the state of the art of multivariate algorithmics and complexity. Increasingly, multivariate algorithmics is having significant practical impact in many application domains, with even more developments on the horizon....
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| Format: | Book |
| Language: | English |
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London
Springer
[2013]
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| Edition: | Softcover reprint of the hardcover 1st edition 2013 |
| Series: | Texts in computer science
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | This comprehensive and self-contained textbook presents an accessible overview of the state of the art of multivariate algorithmics and complexity. Increasingly, multivariate algorithmics is having significant practical impact in many application domains, with even more developments on the horizon. The text describes how the multivariate framework allows an extended dialog with a problem, enabling the reader who masters the complexity issues under discussion to use the positive and negative toolkits in their own research. Features: describes many of the standard algorithmic techniques available for establishing parametric tractability; reviews the classical hardness classes; explores the various limitations and relaxations of the methods; showcases the powerful new lower bound techniques; examines various different algorithmic solutions to the same problems, highlighting the insights to be gained from each approach; demonstrates how complexity methods and ideas have evolved over the past 25 years |
| Item Description: | The field of parameterized complexity/multivariate complexity algorithmics is an exciting and vibrant part of theoretical computer science, responding to the vital need for efficient algorithms in modern society.This comprehensive and self-contained textbook presents an accessible overview of the state of the art of multivariate algorithmics and complexity. Increasingly, multivariate algorithmics is having significant practical impact in many application domains, with even more developments on the horizon. The text describes how the multivariate framework allows an extended dialog with a problem, enabling the reader who masters the complexity issues under discussion to use the positive and negative toolkits in their own research.Topics and features:- Describes many of the standard algorithmic techniques available for establishing parametric tractability- Reviews the classical hardness classes- Explores the various limitations and relaxations of the methods- Showcases the powerful new lower bound techniques- Examines various different algorithmic solutions to the same problems, highlighting the insights to be gained from each approach- Demonstrates how complexity methods and ideas have evolved over the past 25 yearsThis classroom-tested and easy-to-follow textbook/reference is essential reading for the beginning graduate student and advanced undergraduate student. The book will also serve as an invaluable resource for the general computer scientist and the mathematically-aware scientist seeking tools for their research Introduction.- Part I: Parameterized Tractability.- Preliminaries.- The Basic Definitions.- Part II: Elementary Positive Techniques.- Bounded Search Trees.- Kernelization.- More on Kernelization.- Iterative Compression, and Measure and Conquer, for Minimization Problems.- Further Elementary Techniques.- Colour Coding, Multilinear Detection, and Randomized Divide and Conquer.- Optimization Problems, Approximation Schemes, and Their Relation to FPT.- Part III: Techniques Based on Graph Structure.- Treewidth and Dynamic Programming.- Heuristics for Treewidth.- Automata and Bounded Treewidth.- Courcelle's Theorem.- More on Width-Metrics: Applications and Local Treewidth.- Depth-First Search and the Plehn-Voigt Theorem.- Other Width Metrics.- Part IV: Exotic Meta-Techniques.- Well-Quasi-Orderings and the Robertson-Seymour Theorems.- The Graph Minor Theorem.- Applications of the Obstruction Principle and WQOs.- Part V: Hardness Theory.- Reductions.- TheBasic Class W[1] and an Analog of Cook's Theorem.- Other Hardness Results.- The W-Hierarchy.- The Monotone and Antimonotone Collapses.- Beyond W-Hardness.- k-Move Games.- Provable Intractability: The Class XP.- Another Basis.- Part VI: Approximations, Connections, Lower Bounds.- The M-Hierarchy, and XP-optimality.- Kernelization Lower Bounds.- Part VII: Further Topics.- Parameterized Approximation.- Parameterized Counting and Randomization.- Part VIII: Research Horizons.- Research Horizons.- Part IX Appendices.- Appendix 1: Network Flows and Matchings.- Appendix 2: Menger's Theorems. |
| Physical Description: | xxx, 763 Seiten Illustrationen, Diagramme 1199 gr |
| ISBN: | 9781447171645 |
Staff View
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| 500 | |a The field of parameterized complexity/multivariate complexity algorithmics is an exciting and vibrant part of theoretical computer science, responding to the vital need for efficient algorithms in modern society.This comprehensive and self-contained textbook presents an accessible overview of the state of the art of multivariate algorithmics and complexity. Increasingly, multivariate algorithmics is having significant practical impact in many application domains, with even more developments on the horizon. The text describes how the multivariate framework allows an extended dialog with a problem, enabling the reader who masters the complexity issues under discussion to use the positive and negative toolkits in their own research.Topics and features:- Describes many of the standard algorithmic techniques available for establishing parametric tractability- Reviews the classical hardness classes- Explores the various limitations and relaxations of the methods- Showcases the powerful new lower bound techniques- Examines various different algorithmic solutions to the same problems, highlighting the insights to be gained from each approach- Demonstrates how complexity methods and ideas have evolved over the past 25 yearsThis classroom-tested and easy-to-follow textbook/reference is essential reading for the beginning graduate student and advanced undergraduate student. The book will also serve as an invaluable resource for the general computer scientist and the mathematically-aware scientist seeking tools for their research | ||
| 500 | |a Introduction.- Part I: Parameterized Tractability.- Preliminaries.- The Basic Definitions.- Part II: Elementary Positive Techniques.- Bounded Search Trees.- Kernelization.- More on Kernelization.- Iterative Compression, and Measure and Conquer, for Minimization Problems.- Further Elementary Techniques.- Colour Coding, Multilinear Detection, and Randomized Divide and Conquer.- Optimization Problems, Approximation Schemes, and Their Relation to FPT.- Part III: Techniques Based on Graph Structure.- Treewidth and Dynamic Programming.- Heuristics for Treewidth.- Automata and Bounded Treewidth.- Courcelle's Theorem.- More on Width-Metrics: Applications and Local Treewidth.- Depth-First Search and the Plehn-Voigt Theorem.- Other Width Metrics.- Part IV: Exotic Meta-Techniques.- Well-Quasi-Orderings and the Robertson-Seymour Theorems.- The Graph Minor Theorem.- Applications of the Obstruction Principle and WQOs.- Part V: Hardness Theory.- Reductions.- TheBasic Class W[1] and an Analog of Cook's Theorem.- Other Hardness Results.- The W-Hierarchy.- The Monotone and Antimonotone Collapses.- Beyond W-Hardness.- k-Move Games.- Provable Intractability: The Class XP.- Another Basis.- Part VI: Approximations, Connections, Lower Bounds.- The M-Hierarchy, and XP-optimality.- Kernelization Lower Bounds.- Part VII: Further Topics.- Parameterized Approximation.- Parameterized Counting and Randomization.- Part VIII: Research Horizons.- Research Horizons.- Part IX Appendices.- Appendix 1: Network Flows and Matchings.- Appendix 2: Menger's Theorems. | ||
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Contents Part I 1 Preliminaries. 1.1 1.2 1.3 1.4 1.5 2 Basic Classical Complexity. Advice Classes. Valiant-Vazirani and BPP. Historical Notes. Summary. The Basic Definitions. 2.1 2.2 2.3 2.4 2.5 Part II 3 Parameterized Tractability The Basic Definition. The Other Flavors of Parameterized Tractability. Exercises. Historical Notes. Summary. 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 15 15 16 19 20 21 Elementary Positive Techniques Bounded Search Trees. 3.1 3.2 3 3 7 9 12 13 The Basic Method. Vertex
Cover. 3.2.1 A Basic Search Tree. 3.2.2 Shrinking the Search Tree. Planar Independent Set. Planar Dominating Set and Annotated Reduction Rules . 3.4.1 The Basic Analysis. 3.4.2 An Improved Analysis . Feedback Vertex Set. Closest String. Jump Number and Scheduling. Exercises. Historical Notes. Summary. 25 25 25 25 26 28 29 29 31 33 36 37 43 46 47 xxi
xxii 4 Contents Kernelization. 4.1 The Basic Method. 4.2 Heuristics and Applications I. Shrink the Kernel: The Nemhauser-Trotter Theorem. Interleaving . Heuristics and Applications II. Heuristics and Applications III. Definition of a Kernel. k-MAXIMUM Leaf Spanning Tree. Hereditary Properties and Leizhen Cai’s Theorem. Maximum Agreement Forest. 4.10.1 Phylogeny. 4.10.2 The Algorithm and Correctness. 4.10.3 Analysis. 4.11 Exercises. 4.12 Historical Notes. 4.13 Summary. 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 5 More on
Kernelization. 5.1 5.2 5.3 5.4 5.5 6 Turing Kernelization. 5.1.1 Rooted k-LEAF Outbranching. 5.1.2 s-t and r-r Numberings. 5.1.3 A Second Combinatorial Bound. 5.1.4 A Quadratic Kernel. 5.1.5 k-LEAF Outbranching and Turing Kernels . Crown Reductions. Exercises. Historical Notes. Summary. Iterative Compression, and Measure and Conquer, for Minimization Problems . 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 Iterative Compression: The Basic Technique. Edge Bipartization . Heuristics and Algorithmic Improvements. Measure and Conquer. FeedbackVertexSet. 6.5.1 The Simplified Algorithm. 6.5.2 The 3-Regular
Case. 6.5.3 An Improved Running Time Using Measure and Conquer. Exercises. Historical Remarks. Summary. 49 49 54 55 59 60 62 63 64 67 69 69 74 81 81 88 89 91 91 91 92 95 96 99 100 104 106 106 107 107 109 112 113 117 117 121 125 128 129 130
Contents xxh'i 7 Further Elementary Techniques. 7.1 Methods Based on Induction . 7.1.1 The Extremal Method. 7.1.2 k-LEAF SPANNING TREE, Revisited. 7.2 Greedy Localization. 7.2.1 3-Dimensional Matching. 7.3 Bounded Variable Integer Programming . 7.4 Exercises. 7.5 Historical Notes. 7.6 Summary. 131 131 131 132 134 135 137 139 141 141 8 Color Coding, Multilinear Detection, and Randomized Divide and Conquer. 143 8.1 Introduction. 8.1.1 k-PATH . 8.1.2 Dynamic Programming. 8.2 The Randomized Technique. 8.3 De-randomizing. 8.3.1 Multidimensional Matching. 8.4
Speeding Things up with Multilinear Detection. 143 144 144 144 145 147 148 8.7 8.4.1 Group Algebras over Z2 . Randomized Divide and Conquer. Divide and Color. 8.6.1 The Algorithm and the Kernel . 8.6.2 Probability of a Good Coloring. 8.6.3 Solving a Colored Instance. 8.6.4 Derandomization with Universal Coloring Families . Solving MAX-r-SAT Above a Tight Lower Bound . 149 153 155 156 157 158 160 162 8.8 8.9 8.10 Exercises. Historical Notes. Summary. 165 168 170 8.5 8.6 9 Optimization Problems, Approximation Schemes, and Their Relation to FPT. 171 9.1 Optimization. 9.2 Optimization Problems . 9.3 How FPT and Optimization Problems Relate:Part I. 9.4 The Classes MAX SNP, MIN F+Πι (h) and FPT. 9.5
Exercises. 9.6 Historical Notes. 9.7 Summary. 171 171 172 176 181 182 182
xxiv Contents Part III Techniques Based on Graph Structure 10 Treewidth and Dynamic Programming. 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 11 Heuristics for Treewidth. 11.1 11.2 11.3 11.4 11.5 11.6 11.7 12 Basic Facts About Treewidth. 10.1.1 Introduction. 10.1.2 The Basic Definitions. Exercises. Algorithms for Graphs of Bounded Treewidth . Exercises. Bodlaender’s Theorem. Exercises. Historical Notes. Summary. Introduction. Separators. Perfect Elimination . Reduction
Rules. Exercises. Historical Notes. Summary. Methods via Automata and Bounded Treewidth. 12.1 Introduction. 12.2 Deterministic Finite Automata. 12.2.1 Historical Notes. 12.2.2 Exercises . 12.3 Nondeterministic Finite Automata. 12.3.1 Historical Notes. 12.3.2 Exercises . 12.4 Regular Languages. 12.4.1 Historical Notes. 12.4.2 Exercises . 12.5 The Myhill-Nerode Theorem and the Method of Test Sets . . . 12.5.1 Historical Notes. 12.5.2 Exercises . 12.6 Tree
Automata. 12.6.1 Historical Notes. 12.6.2 Exercises . 12.7 Parse Trees for Graphs of Bounded Treewidth and an Analogue of the Myhill-Nerode Theorem. 12.7.1 Historical Notes. 12.7.2 Exercises . 12.8 Summary. 185 185 185 186 189 190 193 195 202 202 203 205 205 206 207 209 211 211 211 213 213 213 216 216 216 221 221 222 226 226 227 234 235 237 246 246 247 263 263 264
Contents XXV 13 Courcelle’s Theorem. 13.1 The Basic Theorem. 13.2 Implementing Courcelle’sTheorem. 13.3 Seese’s Theorem. 13.4 Notes on MS 1 Theory. 13.5 Exercises. 13.6 Historical Notes. 13.7 Summary. 14 More on Width-Metrics: Applications and Local Treewidth. 279 14.1 Applications of Width Metrics toObjects Other than Graphs . . 279 14.1.1 Logic . 280 14.1.2 Matroid Treewidth and Branchwidth. 281 14.1.3 Knots, Links, and Polynomials. 282 14.2 Local Treewidth. 284 14.2.1 Definitions. 284 14.2.2 The Frick-Grohe Theorem. 286 14.3 Exercises. 288 14.4
Historical Notes. 288 14.5 Summary. 289 265 265 272 272 274 275 276 278 15 Depth-First Search and the Plehn-Voigt Theorem. 15.1 Depth-First Search. 15.2 Exercises. 15.3 Bounded-Width Subgraphs, the Plehn-Voigt Theorem, and Induced Subgraphs. 15.4 Exercises. 15.5 Historical Remarks. 15.6 Summary. 291 291 293 Other Width Metrics. 16.1 Branchwidth. 16.2 Basic Properties of Branchwidth . 16.3 Dynamic Programming and Branchwidth. 16.4 Fast Matrix Multiplication and Dynamic Programming. 16.4.1 Improving Things Using Matrix Multiplication . . . 16.5 Cliquewidth and Rankwidth. 16.6 Directed
Graphs. 16.7 d-Degeneracy . 16.8 Exercises. 16.9 Historical Notes. 16.10 Summary. 301 301 302 303 306 307 309 312 313 315 316 316 16 295 299 300 300
χχνί Contents Part IV Exotic Meta-techniques 17 Well-Quasi-Orderings and the Robertson-Seymour Theorems . . . 17.1 Basics of Well-Quasi-Orderings Theory. 17.2 Connections with Automata Theoryand Boundaried Graphs . . 17.3 Exercises. 17.4 Historical Notes. 17.5 Summary. 319 319 333 336 337 338 18 The Graph Minor Theorem. 18.1 Introduction. 18.2 Excluding a Forest. 18.3 Thomas’ Lemma. 18.4 The Graph Minor Theorem. 18.5 The Immersion and Topological Orders. 18.6 The Summary. 18.7 Exercises. 18.8 Historical Notes. 18.9 Summary. 339 339 340 342 345 347 348 349 350 350 19 Applications
of the Obstruction Principle and WQOs . 19.1 Methods for Tractability. 19.2 Effectivizations of Obstruction-Based Methods. 19.2.1 Effectivization by Self-reduction. 19.2.2 Effectivization by Obstruction Set Computation . . . 19.3 The Irrelevant Vertex Technique. 19.4 Protrusions. 19.4.1 Informal Description. 19.4.2 Overview of the Protrusion Based Meta-kernelization Results. 367 19.4.3 Overview of the Methods. 19.5 Exercises. 19.6 Historical Remarks. 19.7 Summary. 351 351 357 357 361 364 365 366 Part V 20 368 369 371 372 Hardness Theory Reductions . 20.1 Introduction. 20.2 ParameterizedReductions. 20.3
Exercises. 20.4 Historical Notes. 20.5 Summary. 375 375 377 380 382 382
Contents 21 xxvii The Basic Class W[l] and an Analog of Cook’s Theorem. 383 Introduction. 383 21.1 21.2 Short Turing Machine Acceptance 22 . 384 21.3 Exercises. 401 21.4 Historical Notes. 405 21.5 Summary. 406 Some Other W[l] Hardness Results 22.1 22.2 The VC Dimension 22.3 23 25 407 407 . 412 Logic Problems . 414 22.4 Exercises. 424 22.5 Historical Notes. 426 22.6 Summary. 426 The W-Hierarchy. 427 23.1 Introduction. 427 23.2 The Normalization Theorem. 23.2.1 The Dominating Set Reduction. 429 429 The Proof of the Normalization
Theorem. 434 23.2.2 24 . Perfect Code and the Turing Way to W-Membership . 23.3 Monotone and Antimonotone Formulas. 23.4 The W*-Hierarchy and Generalized Normalization to W*[i] . . 444 446 23.4.1 w* Normalization. 447 23.4.2 An Improved Characterization of W[l]. 448 23.5 Exercises. 455 23.6 Historical Notes. 459 23.7 Summary. 459 The Monotone and Antimonotone Collapse Theorems: Monotone W{2t + 1] = W[2t] and Antimonotone W[2t + 2] = W[2t + 1]. 461 24.1 Results. 461 24.2 Historical Notes. 471 24.3 Summary. 471 Beyond Иф]-Hardness. 473 25.1 W[P] and W[SAT]. 473 25.2 Exercises. 485
25.3 Historical Remarks. 488 25.4 Summary. 489
xxviii 26 Contents Fixed Parameter Analogues of PS PACE and k-Move Games . 26.1 26.2 26.3 26.4 26.5 26.6 26.7 27 Provable Intractability: The Class XP. 27.1 27.2 27.3 27.4 27.5 27.6 28 Introduction. k-Move Games. AW[*] . Relational Databases. Exercises. Historical Notes. Summary. Introduction and X Classes . Pebble Games. Other XP-Completeness Results. Exercises. Historical Remarks. Summary. Another Basis for the W-Hierarchy and the Tradeoff Theorem . . 28.1 28.2 28.3 28.4 Results.
Exercises. Historical Notes. Summary. 491 491 491 495 499 502 506 507 509 509 510 517 518 518 519 521 521 530 531 531 Part VI Approximations, Connections, Lower Bounds 29 The Μ -Hierarchy, and XP-Optimality. 29.1 29.2 29.3 29.4 29.5 29.6 29.7 29.8 29.9 29.10 29.11 29.12 29.13 Introduction. The W-Hierarchy and SUBEXP Time . The Af-Hierarchy. Parametric Miniatures. The Sparsification Lemma. 29.5.1 Statement of the Lemma. 29.5.2 Using the Lemma for O*(2°^) Lower Bounds . . . 29.5.3 No O*((l + e/) Algorithm for Vertex Cover . The Proof of the Sparsification Lemma. XP-Optimality. Treewidth Lower Bounds. The Strong Exponential Time Hypothesis. Subexponential Algorithms and Bidimensionality .
Exercises. Historical Notes. 29.12.1 Prehistory. 29.12.2 History . Summary. 535 535 535 541 542 546 546 546 552 553 556 557 559 561 565 567 567 569 570
Contents 30 xxix Kernelization Lower Bounds . 571 30.1 Introduction. 571 30.2 A Generic Engine for Lower Bounds of Kernels. 572 30.3 Applications of OR-Composition. 577 Notes on Turing Kernels. 579 AND Composition. 579 30.3.1 30.4 30.5 Proof of Drucker’s Theorem. 582 30.5.1 Statistical Distance and Distinguishability . 582 30.5.2 Proof of Theorem 30.5.2 . 583 30.6 Cross-composition. 588 30.7 Unique Identifiers. 592 30.8 Sharpening Bounds . 595 30.9 The Packing Lemma. 596 30.10 Co-nondeterminism. 597 30.11 30.10.1 Co-nondeterministic Composition,and k-RAMSEY 30.10.2 Co-nondeterministic Cross-composition and Hereditary Properties. . 602 Weak Composition and Sharp Lower BoundsRevisited . 30.12 Miniature Parametric Miniatures 597 606
. 612 30.13 Exercises. 615 30.14 Historical Notes. 619 30.15 Summary. 619 Part VII Further Topics 31 Parameterized Approximation . 623 31.1 Introduction. 623 31.2 Pathwidth . 628 31.3 Treewidth . 633 31.4 Parameterized OnlineAlgorithms and Incremental Computing . 635 31.4.1 Coloring. 636 31.4.2 Online ColoringGraphs of Bounded Pathwidth . . . 636 31.5 Parameterized Inapproximability. 639 31.6 Exercises. 641 31.7 Historical Notes. 643 31.8 Summary. 644
Contents XXX 32 Parameterized Counting and Randomization. 32.1 32.2 32.3 32.4 32.5 32.6 32.7 32.8 32.9 32.10 Introduction. Classical Counting Problems and #P. #W[1]—A Parameterized Counting Class. The Counting Analog of Cook’s Theorem. The #W-Hierarchy. An Analog of Valiant’s Theorem. Parameterized Randomization. Exercises. Historical Notes. Summary. 645 645 646 648 649 657 658 663 670 671 673 Part VIII Research Horizons 33 Research Horizons. 33.1 33.2 33.3 33.4 The Most Infamous. Think Positive!. More Tough Customers. Exemplars of Programs. 677 677 679 681 684 Part IX
Appendices Network Flows. 34.1.1 Basic Results. 34.1.2 Exercises . 34.1.3 The Ford-Fulkerson Algorithm. 689 689 689 691 692 34.2 34.3 34.4 34.1.4 Matching Theory. Berge’s Criterion. Edmonds’ Algorithm . Bipartite Graphs and Vertex Cover. 693 695 697 699 34.5 34.6 Matching and Co-graphic Matroids. The Matroid Parity Problem . 700 704 Appendix 2: Menger’s Theorems. Connectivity. Exercises. 705 705 707 References . 709 Index 745 34 Appendix 1: Network Flows and Matchings. 34.1 35 35.1 35.2 |
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| author | Downey, R. G. 1957- |
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| edition | Softcover reprint of the hardcover 1st edition 2013 |
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Fellows</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">Softcover reprint of the hardcover 1st edition 2013</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">London</subfield><subfield code="b">Springer</subfield><subfield code="c">[2013]</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">xxx, 763 Seiten</subfield><subfield code="b">Illustrationen, Diagramme</subfield><subfield code="c">1199 gr</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Texts in computer science</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">The field of parameterized complexity/multivariate complexity algorithmics is an exciting and vibrant part of theoretical computer science, responding to the vital need for efficient algorithms in modern society.This comprehensive and self-contained textbook presents an accessible overview of the state of the art of multivariate algorithmics and complexity. Increasingly, multivariate algorithmics is having significant practical impact in many application domains, with even more developments on the horizon. The text describes how the multivariate framework allows an extended dialog with a problem, enabling the reader who masters the complexity issues under discussion to use the positive and negative toolkits in their own research.Topics and features:- Describes many of the standard algorithmic techniques available for establishing parametric tractability- Reviews the classical hardness classes- Explores the various limitations and relaxations of the methods- Showcases the powerful new lower bound techniques- Examines various different algorithmic solutions to the same problems, highlighting the insights to be gained from each approach- Demonstrates how complexity methods and ideas have evolved over the past 25 yearsThis classroom-tested and easy-to-follow textbook/reference is essential reading for the beginning graduate student and advanced undergraduate student. The book will also serve as an invaluable resource for the general computer scientist and the mathematically-aware scientist seeking tools for their research</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Introduction.- Part I: Parameterized Tractability.- Preliminaries.- The Basic Definitions.- Part II: Elementary Positive Techniques.- Bounded Search Trees.- Kernelization.- More on Kernelization.- Iterative Compression, and Measure and Conquer, for Minimization Problems.- Further Elementary Techniques.- Colour Coding, Multilinear Detection, and Randomized Divide and Conquer.- Optimization Problems, Approximation Schemes, and Their Relation to FPT.- Part III: Techniques Based on Graph Structure.- Treewidth and Dynamic Programming.- Heuristics for Treewidth.- Automata and Bounded Treewidth.- Courcelle's Theorem.- More on Width-Metrics: Applications and Local Treewidth.- Depth-First Search and the Plehn-Voigt Theorem.- Other Width Metrics.- Part IV: Exotic Meta-Techniques.- Well-Quasi-Orderings and the Robertson-Seymour Theorems.- The Graph Minor Theorem.- Applications of the Obstruction Principle and WQOs.- Part V: Hardness Theory.- Reductions.- TheBasic Class W[1] and an Analog of Cook's Theorem.- Other Hardness Results.- The W-Hierarchy.- The Monotone and Antimonotone Collapses.- Beyond W-Hardness.- k-Move Games.- Provable Intractability: The Class XP.- Another Basis.- Part VI: Approximations, Connections, Lower Bounds.- The M-Hierarchy, and XP-optimality.- Kernelization Lower Bounds.- Part VII: Further Topics.- Parameterized Approximation.- Parameterized Counting and Randomization.- Part VIII: Research Horizons.- Research Horizons.- Part IX Appendices.- Appendix 1: Network Flows and Matchings.- Appendix 2: Menger's Theorems.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">This comprehensive and self-contained textbook presents an accessible overview of the state of the art of multivariate algorithmics and complexity. Increasingly, multivariate algorithmics is having significant practical impact in many application domains, with even more developments on the horizon. The text describes how the multivariate framework allows an extended dialog with a problem, enabling the reader who masters the complexity issues under discussion to use the positive and negative toolkits in their own research. Features: describes many of the standard algorithmic techniques available for establishing parametric tractability; reviews the classical hardness classes; explores the various limitations and relaxations of the methods; showcases the powerful new lower bound techniques; examines various different algorithmic solutions to the same problems, highlighting the insights to be gained from each approach; demonstrates how complexity methods and ideas have evolved over the past 25 years</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">bicssc</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Algorithms</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Parametrisierte Komplexität</subfield><subfield code="0">(DE-588)4818897-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Komplexität</subfield><subfield code="0">(DE-588)4135369-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Algorithmus</subfield><subfield code="0">(DE-588)4001183-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Hardcover, Softcover / Mathematik/Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Komplexität</subfield><subfield code="0">(DE-588)4135369-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Algorithmus</subfield><subfield code="0">(DE-588)4001183-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Parametrisierte Komplexität</subfield><subfield code="0">(DE-588)4818897-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Fellows, Michael R.</subfield><subfield code="d">1952-</subfield><subfield code="e">Sonstige</subfield><subfield code="0">(DE-588)1024321916</subfield><subfield code="4">oth</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="o">10.1007/978-1-4471-5559-1</subfield><subfield code="z">978-1-4471-5559-1</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Bamberg - ADAM Catalogue Enrichment</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035208696&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-035208696</subfield></datafield></record></collection> |
| id | DE-604.BV049869188 |
| illustrated | Illustrated |
| indexdate | 2024-12-16T11:03:29Z |
| institution | BVB |
| isbn | 9781447171645 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-035208696 |
| oclc_num | 1466902708 |
| open_access_boolean | |
| owner | DE-473 DE-BY-UBG |
| owner_facet | DE-473 DE-BY-UBG |
| physical | xxx, 763 Seiten Illustrationen, Diagramme 1199 gr |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Springer |
| record_format | marc |
| series2 | Texts in computer science |
| spelling | Downey, R. G. 1957- Verfasser (DE-588)1052125417 aut Fundamentals of parameterized complexity Rodney G. Downey, Michael R. Fellows Softcover reprint of the hardcover 1st edition 2013 London Springer [2013] xxx, 763 Seiten Illustrationen, Diagramme 1199 gr txt rdacontent n rdamedia nc rdacarrier Texts in computer science The field of parameterized complexity/multivariate complexity algorithmics is an exciting and vibrant part of theoretical computer science, responding to the vital need for efficient algorithms in modern society.This comprehensive and self-contained textbook presents an accessible overview of the state of the art of multivariate algorithmics and complexity. Increasingly, multivariate algorithmics is having significant practical impact in many application domains, with even more developments on the horizon. The text describes how the multivariate framework allows an extended dialog with a problem, enabling the reader who masters the complexity issues under discussion to use the positive and negative toolkits in their own research.Topics and features:- Describes many of the standard algorithmic techniques available for establishing parametric tractability- Reviews the classical hardness classes- Explores the various limitations and relaxations of the methods- Showcases the powerful new lower bound techniques- Examines various different algorithmic solutions to the same problems, highlighting the insights to be gained from each approach- Demonstrates how complexity methods and ideas have evolved over the past 25 yearsThis classroom-tested and easy-to-follow textbook/reference is essential reading for the beginning graduate student and advanced undergraduate student. The book will also serve as an invaluable resource for the general computer scientist and the mathematically-aware scientist seeking tools for their research Introduction.- Part I: Parameterized Tractability.- Preliminaries.- The Basic Definitions.- Part II: Elementary Positive Techniques.- Bounded Search Trees.- Kernelization.- More on Kernelization.- Iterative Compression, and Measure and Conquer, for Minimization Problems.- Further Elementary Techniques.- Colour Coding, Multilinear Detection, and Randomized Divide and Conquer.- Optimization Problems, Approximation Schemes, and Their Relation to FPT.- Part III: Techniques Based on Graph Structure.- Treewidth and Dynamic Programming.- Heuristics for Treewidth.- Automata and Bounded Treewidth.- Courcelle's Theorem.- More on Width-Metrics: Applications and Local Treewidth.- Depth-First Search and the Plehn-Voigt Theorem.- Other Width Metrics.- Part IV: Exotic Meta-Techniques.- Well-Quasi-Orderings and the Robertson-Seymour Theorems.- The Graph Minor Theorem.- Applications of the Obstruction Principle and WQOs.- Part V: Hardness Theory.- Reductions.- TheBasic Class W[1] and an Analog of Cook's Theorem.- Other Hardness Results.- The W-Hierarchy.- The Monotone and Antimonotone Collapses.- Beyond W-Hardness.- k-Move Games.- Provable Intractability: The Class XP.- Another Basis.- Part VI: Approximations, Connections, Lower Bounds.- The M-Hierarchy, and XP-optimality.- Kernelization Lower Bounds.- Part VII: Further Topics.- Parameterized Approximation.- Parameterized Counting and Randomization.- Part VIII: Research Horizons.- Research Horizons.- Part IX Appendices.- Appendix 1: Network Flows and Matchings.- Appendix 2: Menger's Theorems. This comprehensive and self-contained textbook presents an accessible overview of the state of the art of multivariate algorithmics and complexity. Increasingly, multivariate algorithmics is having significant practical impact in many application domains, with even more developments on the horizon. The text describes how the multivariate framework allows an extended dialog with a problem, enabling the reader who masters the complexity issues under discussion to use the positive and negative toolkits in their own research. Features: describes many of the standard algorithmic techniques available for establishing parametric tractability; reviews the classical hardness classes; explores the various limitations and relaxations of the methods; showcases the powerful new lower bound techniques; examines various different algorithmic solutions to the same problems, highlighting the insights to be gained from each approach; demonstrates how complexity methods and ideas have evolved over the past 25 years bicssc bisacsh Mathematics Algorithms Parametrisierte Komplexität (DE-588)4818897-9 gnd rswk-swf Komplexität (DE-588)4135369-9 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf Hardcover, Softcover / Mathematik/Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik Komplexität (DE-588)4135369-9 s Algorithmus (DE-588)4001183-5 s Parametrisierte Komplexität (DE-588)4818897-9 s DE-604 Fellows, Michael R. 1952- Sonstige (DE-588)1024321916 oth Erscheint auch als Online-Ausgabe 10.1007/978-1-4471-5559-1 978-1-4471-5559-1 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035208696&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Downey, R. G. 1957- Fundamentals of parameterized complexity bicssc bisacsh Mathematics Algorithms Parametrisierte Komplexität (DE-588)4818897-9 gnd Komplexität (DE-588)4135369-9 gnd Algorithmus (DE-588)4001183-5 gnd |
| subject_GND | (DE-588)4818897-9 (DE-588)4135369-9 (DE-588)4001183-5 |
| title | Fundamentals of parameterized complexity |
| title_auth | Fundamentals of parameterized complexity |
| title_exact_search | Fundamentals of parameterized complexity |
| title_full | Fundamentals of parameterized complexity Rodney G. Downey, Michael R. Fellows |
| title_fullStr | Fundamentals of parameterized complexity Rodney G. Downey, Michael R. Fellows |
| title_full_unstemmed | Fundamentals of parameterized complexity Rodney G. Downey, Michael R. Fellows |
| title_short | Fundamentals of parameterized complexity |
| title_sort | fundamentals of parameterized complexity |
| topic | bicssc bisacsh Mathematics Algorithms Parametrisierte Komplexität (DE-588)4818897-9 gnd Komplexität (DE-588)4135369-9 gnd Algorithmus (DE-588)4001183-5 gnd |
| topic_facet | bicssc bisacsh Mathematics Algorithms Parametrisierte Komplexität Komplexität Algorithmus |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035208696&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT downeyrg fundamentalsofparameterizedcomplexity AT fellowsmichaelr fundamentalsofparameterizedcomplexity |