大葉大學圖書館 |

Genetic theory for cubic graphs[electronic resource] /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	511.5
書名/作者:	Genetic theory for cubic graphs/ by Pouya Baniasadi ... [et al.].
其他作者:	Baniasadi, Pouya.
出版者:	Cham : : Springer International Publishing :, 2016.
面頁冊數:	x, 118 p. : : ill., digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Graph connectivity.
標題:	Graph theory.
標題:	Economics/Management Science.
標題:	Operation Research/Decision Theory.
標題:	Operations Research, Management Science.
標題:	Graph Theory.
ISBN:	9783319196800
ISBN:	9783319196794
內容註:	Genetic Theory for Cubic Graphs -- Inherited Properties of Descendants -- Uniqueness of Ancestor Genes -- Completed Proofs from Chapter 3.
摘要、提要註:	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.
電子資源:	http://dx.doi.org/10.1007/978-3-319-19680-0

Genetic theory for cubic graphs[electronic resource] /
Genetic theory for cubic graphs[electronic resource] /by Pouya Baniasadi ... [et al.]. - Cham :Springer International Publishing :2016. - x, 118 p. :ill., digital ;24 cm. - SpringerBriefs in operations research,2195-0482. - SpringerBriefs in operations research..

Genetic Theory for Cubic Graphs -- Inherited Properties of Descendants -- Uniqueness of Ancestor Genes -- Completed Proofs from Chapter 3.

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.

ISBN: 9783319196800

Standard No.: 10.1007/978-3-319-19680-0doiSubjects--Topical Terms:

651596
Graph connectivity.

LC Class. No.: QA166.243

Dewey Class. No.: 511.5

Genetic theory for cubic graphs[electronic resource] /
LDR:03828nam a2200337 a 4500 001 454260
003 DE-He213
005 20160711154706.0
006 m d
007 cr nn 008maaau
008 161227s2016 gw s 0 eng d
020 $a 9783319196800 $q (electronic bk.)
020 $a 9783319196794 $q (paper)
024 7 $a 10.1007/978-3-319-19680-0 $2 doi
035 $a 978-3-319-19680-0
040 $a GP $c GP
041 0 $a eng
050 4 $a QA166.243
072 7 $a KJT $2 bicssc
072 7 $a KJMD $2 bicssc
072 7 $a BUS049000 $2 bisacsh
082 0 4 $a 511.5 $2 23
090 $a QA166.243 $b .G328 2016
245 0 0 $a Genetic theory for cubic graphs $h [electronic resource] / $c by Pouya Baniasadi ... [et al.].
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2016.
300 $a x, 118 p. : $b ill., digital ; $c 24 cm.
490 1 $a SpringerBriefs in operations research, $x 2195-0482
505 0 $a Genetic Theory for Cubic Graphs -- Inherited Properties of Descendants -- Uniqueness of Ancestor Genes -- Completed Proofs from Chapter 3.
520 $a 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.
650 0 $a Graph connectivity. $3 651596
650 0 $a Graph theory. $3 381176
650 1 4 $a Economics/Management Science. $3 463465
650 2 4 $a Operation Research/Decision Theory. $3 511310
650 2 4 $a Operations Research, Management Science. $3 463666
650 2 4 $a Graph Theory. $3 466209
700 1 $a Baniasadi, Pouya. $3 651595
710 2 $a SpringerLink (Online service) $3 463450
773 0 $t Springer eBooks
830 0 $a SpringerBriefs in operations research. $3 602531
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-19680-0
950 $a Business and Economics (Springer-11643)