Parameterized algorithms:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Cham
Springer
[2015]
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverzeichnis Seite 556 - 576 |
| Beschreibung: | XVII, 613 Seiten Illustrationen, Diagramme |
| ISBN: | 9783319212746 |
Internformat
MARC
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents Part I Basic toolbox 1 Introduction 1.1 Formal definitions.................................................................... 2 Kernelization 2.1 Formal definitions.................................................................... 2.2 Some simple kernels................................................................. 2.2.1 Vertex Cover........................................................... 2.2.2 Feedback Arc Set inTournaments.................... 2.2.3 Edge Clique Cover..................................................... 2.3 Crown decomposition.............................................................. 2.3.1 Vertex Cover............................................................. 2.3.2 Maximum Satisfiability........................................... 2.4 Expansion lemma.................................................................... 2.5 Kernels based on linear programming.................................... 2.0 Sunflower lemma........................................................................ 2.6.1 d-Hitting Set.............................................................. 3 Bounded search trees 3.1 Vertex Cover.......................... 3.2 3.3 3.4 3.5 How to solve recursive relations Feedback Vertex Set . . . . ^ertex Cover Above ԼՐ . . Closest String....................... 4 Iterative compression 4.1 Illustration of the basic technique.......................................... 4.1.1 A few generic steps..................................................... 4.2 Feedback Vertex Set in Tournaments.......................... 4.2.1 Solving Disjoint
Feedback Vertex Set in Tour naments in polynomial time .................................... 4.3 Feedback Vertex Set............................................................... 4.3.1 First algorithm for Disjoint Feedback Vertex Set *4.3.2 haster algorithm for Disjoint Feedback Vertex Set 4.4 Odd Cycle Transversal........................................................ 1 3 12 17 18 20 21 22 25 26 29 29 30 33 38 39 51 53 55 57 60 67 77 78 80 81 83 86 87 88 91 Xlll
XIV CONTENTS 5 Randomized methods in parameterized algorithms 99 5.1 A simple randomized algorithm for Feedback Vertex Set 101 5.2 Color coding............................................................................. 103 5.2.1 A color coding algorithm for Longest Path .... 104 5.3 Random separation......................................................................106 *5.4 A divide and color algorithm for Longest Path............... 108 5.5 A chromatic coding algorithm for d- C ւ и ST E RING............... 113 5.6 Derandomization .................................................................... 117 5.6.1 Basic pseudorandom objects....................................... 118 5.6.2 Derandomization of algorithms based on variants of color coding.................................................................. 120 6 Miscellaneous 6.1 Dynamic programming over subsets....................................... 6.1.1 Set Cover.................................................................. 6.1.2 Steiner Tree............................................................ 6.2 Integer Linear Programming.......................................... 6.2.1 The example of Imbalance....................................... 6.3 Graph minors and the Robertson-Seymour theorem............ 129 130 130 131 135 136 140 7 Treewidth 7.1 Trees, narrow grids, and dynamic programming.................. 7.2 Path and tree decompositions................................................ 7.3 Dynamic programming on graphs of bounded treewidth . . . 7.3.1 Weighted Independent
Set................................. 7.3.2 Dominating Set......................................................... 7.3.3 Steiner Tree............................................................ 7.4 Treewidth and monadic second-order logic........................... 7.4.1 Monadic second-orderlogic on graphs........................ 7.4.2 Courcelle’s theorem...................................................... 7.5 Graph searching, interval and chordal graphs........................ 7.6 Computing treewidth............................................................... 7.6.1 Balanced separators and separations ........................ 7.6.2 An FPT approximationalgorithm for treewidth . . . 7.7 Win/win approaches and planar problems........................... 7.7.1 Grid theorems............................................................... 7.7.2 Bidimensionality ......................................................... 7.7.3 Shifting technique......................................................... *7.8 Irrelevant vertex technique...................................................... 7.9 Beyond treewidth..................................................................... 151 153 157 162 162 168 172 177 178 183 185 190 192 195 199 200 203 211 216 228 Part II Advanced algorithmic techniques 245 8 Finding cuts and separators 247 8.1 Minimum cuts........................................................................... 249
CONTENTS 8.2 8.3 8.4 8.5 8.6 8.7 xv Important cuts ....................................................................... 254 Edge Multiway Cut........................................................... 201 (p, q)-clustering....................................................................... 264 Directed graphs....................................................................... 272 Directed Feedback Vertex Set .................................... 274 Vertex-deletion problems........................................................ 278 9 Advanced kernelization algorithms 9.1 A quadratic kernel for Feedback Vertex Set.................. 9.1.1 Proof of Gallai’s theorem............................................ 9.1.2 Detecting flowers with Gallai’s theorem..................... 9.1.3 Exploiting the blocker ................................................ *9.2 Moments and Мах-Ег-ЅАТ................................................... 9.2.1 Algebraic representation............................................ 9.2.2 Tools from probability theory.................................... 9.2.3 Analyzing moments of X(էծ)....................................... 9.3 Connected Vertex Cover in planar graphs .................. 9.3.1 Plane graphs and Euler’s formula.............................. 9.3.2 A lemma on planar bipartite graphs........................... 9.3.3 The case of Connected Vertex Cover............... 9.4 Turing kernelization................................................................. 9.4.1 A polynomial Turing kernel for Max Leaf Subtree 285 287 290 295 296 299 301 302
304 307 308 309 310 313 315 10 Algebraic techniques: sieves, convolutions, and polynomials 321 10.1 Inclusion exclusion principle................................................... 322 10.1.1 Hamiltonian Cycle ............................................... 323 10.1.2 Steiner Tree........................................................... 324 10.1.3 Chromatic Number ................................................ 326 10.2 Fast zeta and Möbius transforms .......................................... 328 10.3 Fast subset convolution and cover product........................... 331 10.3.1 Counting colorings via fast subset convolution .... 334 10.3.2 Convolutions and cover products in min-sum semirings 334 10.4 Multivariate polynomials......................................................... 337 10.4.1 Longest Path in time 2kn° ֊l ................................. 310 10.4.2 Longest Path in time շk/2n°0) for undirected bi partite graphs.............................................................. 346 *10.4.3 Longest Path in time 2:îA74„o(i) for undirected graphs.......................................................................... 349 11 Improving dynamic programming on tree decompositions 11.1 Applying fast subset convolution............................................. 11.1.1 Counting perfect matchings....................................... 11.1.2 Dominating Set........................................................ 11.2 Connectivity problems........................................................... 11.2.1 Cut Count
.............................................................. *11.2.2 Deterministic algorithms by Gaussian elimination . . 357 358 358 359 361 361 365
CONTENTS 12 Matroids 377 12.1 Classes of matroids.................................................................. 379 12.1.1 Linear matroids and matroid representation............ 379 12.1.2 Representation of uniform matroids........................... 380 12.1.3 Graphic matroids........................................................ 381 12.1.4 Transversal matroids................................................... 382 12.1.5 Direct sum and partition matroids ........................... 383 12.2 Algorithms for matroid problems .......................................... 383 12.2.1 Matroid intersection and matroid parity.................. 386 12.2.2 Feedback Vertex Set in subcubic graphs............ 389 12.3 Representative sets.................................................................. 392 12.3.1 Playing on a matroid................................................... 394 12.3.2 Kernel for d-HiTTiNG Set.......................................... 398 12.3.3 Kernel for d-Set Packing......................................... 399 12.3.4 γ-Matroid Intersection.......................................... 401 12.3.5 Long Directed Cycle............................................. 403 12.4 Representative families for uniform matroids............................409 12.5 Faster Long Directed Cycle............................................... 410 12.6 Longest Path........................................................................ 413 Part III Lower bounds 419 13 Fixed-parameter intractability 421 13.1 13.2 13.3 *13.4 *13.5 13.6 Parameterized
reductions......................................................... 424 Problems at least, as hard as CLIQUE.................................... 426 The W-hierarchy .................................................................... 435 Turing machines........................................................................ 439 Problems complete for W[l] and W[2].................................... 443 Parameterized reductions: further examples ............................448 13.6.1 Reductions keeping the structure of the graph .... 448 13.6.2 Reductions with vertex representation.........................451 13.6.3 Reductions with vertex and edge representation . . . 453 14 Lower bounds based on the Exponential-Time Hypothesis 467 14.1 The Exponential-Time Hypothesis: motivation and basic results....................................................................................... 14.2 ETH and classical complexity................................................ 14.3 ETH and fixed-parameter tractable problems........................ 14.3.1 Immediate consequences for parameterized complexity *14.3.2 Slightly super-exponential parameterized complexity *14.3.3 Double exponential parameterized complexity .... 14.4 ETH and W[l]-hard problems................................................ 14.4.1 Planar and geometric problems................................. *14.5 Lower bounds based on the Strong Exponential-Time Hypothesis................................................................................. 468 473 475 476 477 484 485 489 502
CONTENTS 14.5.1 Hitting Set parameterized by the size of the universe....................................................................... 14.5.2 Dynamic programming on treewidth ........................ 14.5.3 A refined lower bound for Dominating Set............ 15 Lower bounds for kernelization xvii 503 508 514 523 15.1 Compositionality.................................................................... 524 15.1.1 Distillation.................................................................... 525 15.1.2 Composition................................................................. 529 15.1.3 AND-distillations and AND-compositions ...................533 15.2 Examples................................................................................... 534 15.2.1 Instance selector: Set Splitting.............................. 534 15.2.2 Polynomial parameter transformations: COLORFUL Graph Motif and Steiner Tree ........................ 537 15.2.3 A more involved one: Set Cover................................ 540 15.2.4 Structural parameters: CLIQUE parameterized by the vertex cover number ..................................................... 544 15.3 Weak compositions................................................................. 547 References 556 Appendix 577 Notation 577 Problem definitions 581 Index 599 Author index 609
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| id | DE-604.BV042776965 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T07:09:23Z |
| institution | BVB |
| isbn | 9783319212746 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028207103 |
| oclc_num | 920804734 |
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| physical | XVII, 613 Seiten Illustrationen, Diagramme |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | Springer |
| record_format | marc |
| spelling | Parameterized algorithms Marek Cygan ... Cham Springer [2015] © 2015 XVII, 613 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Literaturverzeichnis Seite 556 - 576 Algorithmus (DE-588)4001183-5 gnd rswk-swf Programmierung (DE-588)4076370-5 gnd rswk-swf Algorithmus (DE-588)4001183-5 s Programmierung (DE-588)4076370-5 s DE-604 Cygan, Marek 1984- Sonstige (DE-588)1064353231 oth Erscheint auch als Online-Ausgabe 978-3-319-21275-3 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028207103&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Parameterized algorithms Algorithmus (DE-588)4001183-5 gnd Programmierung (DE-588)4076370-5 gnd |
| subject_GND | (DE-588)4001183-5 (DE-588)4076370-5 |
| title | Parameterized algorithms |
| title_auth | Parameterized algorithms |
| title_exact_search | Parameterized algorithms |
| title_full | Parameterized algorithms Marek Cygan ... |
| title_fullStr | Parameterized algorithms Marek Cygan ... |
| title_full_unstemmed | Parameterized algorithms Marek Cygan ... |
| title_short | Parameterized algorithms |
| title_sort | parameterized algorithms |
| topic | Algorithmus (DE-588)4001183-5 gnd Programmierung (DE-588)4076370-5 gnd |
| topic_facet | Algorithmus Programmierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028207103&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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