By H. T. Lau

In fresh years researchers have spent a lot attempt in constructing effective heuristic algorithms for fixing the category of NP-complete difficulties that are largely believed to be inherently intractable from the computational standpoint. even though algorithms were designed and are infamous between researchers, machine courses are both no longer carried out on desktops or very tricky to acquire. the aim of this booklet is to supply a resource of FORTRAN coded algorithms for a particular variety of recognized combinatorial optimization difficulties. The ebook is meant for use as a supplementary textual content in combinatorial algorithms, community optimization, operations examine and administration technology. furthermore, a brief description on each one set of rules will let the e-book for use as a handy reference. This paintings should not have been attainable with no the superb amenities of Bell-Northern examine, Canada. H. T. Lau lIe des Soeurs Quebec, Canada August 1986 CONTENTS web page advent half I. INTEGER PROGRAMMING bankruptcy 1. Integer Linear Programming bankruptcy 2. Zero-one Linear Programming 30 bankruptcy three. Zero-one Knapsack challenge 38 half II. community layout bankruptcy four. touring Salesman challenge fifty two bankruptcy five. Steiner Tree challenge eighty one bankruptcy 6. Graph Partitioning ninety eight bankruptcy 7. K-Median situation 106 bankruptcy eight. K-Center place 114 checklist of Subroutines 123 Bibliographic Notes 124 creation Following the based thought of NP-comp1eteness, the assumption of constructing effective heuristic algorithms has been gaining its reputation and significance.

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N. N. N. N. N. 59 Subroutine EULER Parameters In pu t N number of nodes in the graph. M number of edges in the graph. IN 0 DE, JNODE each is an integer vector of length M; the two end nodes of edge i in the graph are stored in for i=l,l', ... ,M; INODE(i), JNODE(i) the node and edge numbers of the input graph can be numbered in any order. Output: LOOP integer vector of length M containing the Euler circuit. Working Storages: IWORKl integer vector of length M; keeps track of the next end node of the arc being traversed.

M number of edges in the graph. IN 0 DE, JNODE each is an integer vector of length M; the two end nodes of edge i in the graph are stored in for i=l,l', ... ,M; INODE(i), JNODE(i) the node and edge numbers of the input graph can be numbered in any order. Output: LOOP integer vector of length M containing the Euler circuit. Working Storages: IWORKl integer vector of length M; keeps track of the next end node of the arc being traversed. IWORK2 integer vector of length M; IWORK2(i) indicates whether arc IWORK3 has been visited.

FALSE. IWK6(I) 0 WORK1(1,1) O. WORK1(2,1) O. WORK2 (l , 1 ) 0. DO 140 I = 2, ISUB WORK1(1,I) = BIG I = IWK4(l) + 1 WORK1(1,I) = WORK3(1) IWK6 (1) = 1 IWK7 (l, I) = 1 GOTO 120 49 SWITCH = . TRUE. LE. NOT. SWITCH DO 160 I = 2, ISUB IROW = I _. LT. LT. LE. NE. FALSE. GT. GT. GT. 0) THEN RHS B - WORK1(ICOL2,ISUB) J = 1 1 IWK5(I) . TRUE. GE. LE. LE. LT. LT. GE. GT. GE. 2) THEN ATEMP = A(Jl) JPONT = IPOINT(Jl) A( Jl) = A(1) IPOINT(Jl) = IPOINT(l) Jl = Jl - 1 J2 = J3 GOTO 20 ENDIF RETURN ElIoTI J4 + 1 Chapter 4 TRAVELING SALESMAN PROBLEM A.