Genetic Theory for Cubic Graphs:
Gespeichert in:
Hauptverfasser: | , , , |
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Format: | Elektronisch E-Book |
Sprache: | English |
Veröffentlicht: |
Cham
Springer
[2016]
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Schriftenreihe: | SpringerBriefs in Operations Research
|
Schlagworte: | |
Online-Zugang: | FMH01 HTW01 UBR01 UBY01 Volltext Inhaltsverzeichnis Abstract |
Beschreibung: | 1 Online-Ressource (X, 118 Seiten) Diagramme |
ISBN: | 9783319196800 9783319196794 |
ISSN: | 2195-0504 |
DOI: | 10.1007/978-3-319-19680-0 |
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Datensatz im Suchindex
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adam_text | GENETIC THEORY FOR CUBIC GRAPHS
/ BANIASADI, POUYA
: 2016
TABLE OF CONTENTS / INHALTSVERZEICHNIS
GENETIC THEORY FOR CUBIC GRAPHS
INHERITED PROPERTIES OF DESCENDANTS
UNIQUENESS OF ANCESTOR GENES
COMPLETED PROOFS FROM CHAPTER 3
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
GENETIC THEORY FOR CUBIC GRAPHS
/ BANIASADI, POUYA
: 2016
ABSTRACT / INHALTSTEXT
THIS BOOK WAS MOTIVATED BY THE NOTION THAT SOME OF THE UNDERLYING
DIFFICULTY IN CHALLENGING INSTANCES OF GRAPH-BASED PROBLEMS (E.G., THE
TRAVELING SALESMAN PROBLEM) MAY BE “INHERITED” FROM SIMPLER GRAPHS
WHICH – IN AN APPROPRIATE SENSE – COULD BE SEEN AS “ANCESTORS”
OF THE GIVEN GRAPH INSTANCE. THE AUTHORS PROPOSE A PARTITIONING OF THE
SET OF UNLABELED, CONNECTED CUBIC GRAPHS INTO TWO DISJOINT SUBSETS NAMED
GENES AND DESCENDANTS, WHERE THE CARDINALITY OF THE DESCENDANTS
DOMINATES THAT OF THE GENES. THE KEY DISTINCTION BETWEEN THE TWO SUBSETS
IS THE PRESENCE OF SPECIAL EDGE CUT SETS, CALLED CUBIC CRACKERS, IN THE
DESCENDANTS. THE BOOK BEGINS BY PROVING THAT ANY GIVEN DESCENDANT MAY BE
CONSTRUCTED BY STARTING FROM A FINITE SET OF GENES AND INTRODUCING THE
REQUIRED CUBIC CRACKERS THROUGH THE USE OF SIX SPECIAL OPERATIONS,
CALLED BREEDING OPERATIONS. IT SHOWS THAT EACH BREEDING OPERATION IS
INVERTIBLE, AND THESE INVERSE OPERATIONS ARE EXAMINED.IT IS THEREFORE
POSSIBLE, FOR ANY GIVEN DESCENDANT, TO IDENTIFY A FAMILY OF GENES THAT
COULD BE USED TO GENERATE THE DESCENDANT. THE AUTHORS REFER TO SUCH A
FAMILY OF GENES AS A “COMPLETE FAMILY OF ANCESTOR GENES” FOR THAT
PARTICULAR DESCENDANT. THE BOOK PROVES THE FUNDAMENTAL, ALTHOUGH QUITE
UNEXPECTED, RESULT THAT ANY GIVEN DESCENDANT HAS EXACTLY ONE COMPLETE
FAMILY OF ANCESTOR GENES. THIS RESULT INDICATES THAT THE PARTICULAR
COMBINATION OF BREEDING OPERATIONS USED STRIKES THE RIGHT BALANCE
BETWEEN ENSURING THAT EVERY DESCENDANT MAY BE CONSTRUCTED WHILE
PERMITTING ONLY ONE GENERATING SET. THE RESULT THAT ANY DESCENDANT CAN
BE CONSTRUCTED FROM A UNIQUE SET OF ANCESTOR GENES INDICATES THAT MOST
OF THE STRUCTURE IN THE DESCENDANT HAS BEEN, IN SOME WAY, INHERITED FROM
THAT, VERY SPECIAL, COMPLETE FAMILY OF ANCESTOR GENES, WITH THE
REMAINING STRUCTURE INDUCED BY THE BREEDING OPERATIONS.AFTER
ESTABLISHING THIS, THE AUTHORS PROCEED TO INVESTIGATE A NUMBER OF GRAPH
THEORETIC PROPERTIES: HAMILTONICITY, BIPARTITENESS, AND PLANARITY, AND
PROVE RESULTS LINKING PROPERTIES OF THE DESCENDANT TO THOSE OF THE
ANCESTOR GENES. THEY DEVELOP NECESSARY (AND IN SOME CASES, SUFFICIENT)
CONDITIONS FOR A DESCENDANT TO CONTAIN A PROPERTY IN TERMS OF THE
PROPERTIES OF ITS ANCESTOR GENES. THESE RESULTS MOTIVATE THE DEVELOPMENT
OF PARALLELIZABLE HEURISTICS THAT FIRST DECOMPOSE A GRAPH INTO ANCESTOR
GENES, AND THEN CONSIDER THE GENES INDIVIDUALLY. IN PARTICULAR, THEY
PROVIDE SUCH A HEURISTIC FOR THE HAMILTONIAN CYCLE PROBLEM.
ADDITIONALLY, A FRAMEWORK FOR CONSTRUCTING GRAPHS WITH DESIRED
PROPERTIES IS DEVELOPED, WHICH SHOWS HOW MANY (KNOWN) GRAPHS THAT
CONSTITUTE COUNTEREXAMPLES OF CONJECTURES COULD BE EASILY FOUND
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
any_adam_object | 1 |
author | Baniasadi, Pouya Ejov, Vladimir Filar, Jerzy A. 1949- Haythorpe, Michael |
author_GND | (DE-588)1088807321 (DE-588)122097599 |
author_facet | Baniasadi, Pouya Ejov, Vladimir Filar, Jerzy A. 1949- Haythorpe, Michael |
author_role | aut aut aut aut |
author_sort | Baniasadi, Pouya |
author_variant | p b pb v e ve j a f ja jaf m h mh |
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owner | DE-2070s DE-1043 DE-Aug4 DE-573 DE-1049 DE-703 DE-473 DE-BY-UBG DE-29 DE-863 DE-BY-FWS DE-862 DE-BY-FWS DE-92 DE-739 DE-824 DE-M347 DE-898 DE-BY-UBR DE-634 DE-1046 DE-83 DE-859 DE-861 DE-523 DE-355 DE-BY-UBR DE-706 |
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physical | 1 Online-Ressource (X, 118 Seiten) Diagramme |
psigel | ZDB-2-BUM ZDB-2-BUM_2016 |
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publisher | Springer |
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series2 | SpringerBriefs in Operations Research |
spellingShingle | Baniasadi, Pouya Ejov, Vladimir Filar, Jerzy A. 1949- Haythorpe, Michael Genetic Theory for Cubic Graphs Business Operations research Decision making Management science Graph theory Business and Management Operation Research/Decision Theory Operations Research, Management Science Graph Theory Wirtschaft Graphentheorie (DE-588)4113782-6 gnd |
subject_GND | (DE-588)4113782-6 |
title | Genetic Theory for Cubic Graphs |
title_auth | Genetic Theory for Cubic Graphs |
title_exact_search | Genetic Theory for Cubic Graphs |
title_full | Genetic Theory for Cubic Graphs Pouya Baniasadi, Vladimir Ejov, Jerzy A. Filar, Michael Haythorpe |
title_fullStr | Genetic Theory for Cubic Graphs Pouya Baniasadi, Vladimir Ejov, Jerzy A. Filar, Michael Haythorpe |
title_full_unstemmed | Genetic Theory for Cubic Graphs Pouya Baniasadi, Vladimir Ejov, Jerzy A. Filar, Michael Haythorpe |
title_short | Genetic Theory for Cubic Graphs |
title_sort | genetic theory for cubic graphs |
topic | Business Operations research Decision making Management science Graph theory Business and Management Operation Research/Decision Theory Operations Research, Management Science Graph Theory Wirtschaft Graphentheorie (DE-588)4113782-6 gnd |
topic_facet | Business Operations research Decision making Management science Graph theory Business and Management Operation Research/Decision Theory Operations Research, Management Science Graph Theory Wirtschaft Graphentheorie |
url | https://doi.org/10.1007/978-3-319-19680-0 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028634951&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028634951&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
work_keys_str_mv | AT baniasadipouya genetictheoryforcubicgraphs AT ejovvladimir genetictheoryforcubicgraphs AT filarjerzya genetictheoryforcubicgraphs AT haythorpemichael genetictheoryforcubicgraphs |