Shortest Connectivity: An Introduction with Applications in Phylogeny
Springer Science & Business Media, 2004. 11. 19. - 268페이지
The aim in this graduate level text is to outline the key mathematical concepts that underpin these important questions in applied mathematics. These concepts involve discrete mathematics (particularly graph theory), optimization, computer science, and several ideas in biology.
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TWO CLASSICAL OPTIMIZATION PROBLEMS
12 MINIMUM SPANNING TREES
22 EXAMPLES AND EXERCISES
24 A FIRST ANALYSIS OF STEINERS PROBLEM
25 STEINERS PROBLEM IN GRAPHS
WHAT DOES SOLUTION MEAN?
53 APPLICATIONS AND RELATED QUESTIONS
AN ANALYSIS OF STEINERS PROBLEM IN PHYLOGENETIC SPACES
62 MORE ABOUT TREES
63 CLUSTER ANALYSIS
64 SPANNING TREES
65 COUNTING THE ELEMENTS IN DISCRETE METRIC SPACES
66 FERMATS PROBLEM IN SEVERAL DISCRETE METRIC SPACES
TREE BUILDING ALGORITHMS
32 DOES A SOLUTION EXIST?
33 DOES AN ALGORITHM EXIST?
34 DOES AN EFFICIENT ALGORITHM EXIST?
35 DOES AN APPROXIMATION EXIST?
NETWORK DESIGN PROBLEMS
42 Several Variants
A NEW CHALLENGE THE PHYLOGENY
51 PHYLOGENETIC TREES
52 PHYLOGENETIC SPACES
기타 출판본 - 모두 보기
algorithm alignment alphabet ancestor applications approach approximation assume Banach spaces binary biology bounded called characters classification collection common complete compute connected Consequently consider construction contains cost create cycle defined denotes describe determined discuss distance edges equal Euclidean plane evolution evolutionary exactly example exists facts finite set function geometric given points gives graph G Hence holds integer interested internal known labelled least leaves length letters mathematical matrix means measure method metric space minimal minimum spanning tree Moreover namely Note Observation optimal pair particular path phylogenetic tree polynomial positive possible precisely procedure proof properties question represent rooted satisfies scoring sense sequences set of points shortest similarity solution solved species Steiner points Steiner ratio Steiner's Problem structure subset Theorem theory Torricelli point tree triangle true vertex vertices