# JOB SEQUENCING

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Education

Published on March 6, 2009

Author: ankush85

Source: authorstream.com

### A FASTER IMPLEMENTATION OF JS (Contd..) :

34 A FASTER IMPLEMENTATION OF JS (Contd..) For i ?1 to n do // use greedy rules // j ? FIND (min (n, D(i)) // F(j) is the nearest free slot if F(j) ? 0 // if F(j) ? 0 then k? k+1 ; J(k)?i All slots are not occupied //select job i // L ? Find (F(j)-1); call union (L, j) F(j)?F(L) // j may be new root // endif repeat end FJS

### A FASTER IMPLEMENTATION OF JS (Contd..) :

35 A FASTER IMPLEMENTATION OF JS (Contd..) It is F(j) –1 because you need to union J with I which is F(j) -1. F(i) is a value for a set of slots with l which is F(j)-1 F(k) = ni for all slots in the set k. ni is that largest integer such that ni ? i and slot ni is free F(1)=1 [0 1] F(2)=2 [1 2] P(i)= is the number of nodes in the tree respectively the set with slot .

### A FASTER IMPLEMENTATION OF JS (Contd..) :

36 A FASTER IMPLEMENTATION OF JS (Contd..) Complexity of algorithm FJS As there are n unions and 2n finds, in the for loop the computing time is 0(n ?(2n , n)) ? (m, n) m ? n is related to Ackermal function ? (m,n)= min {z ? 1/A(3, 4[m/n]) > logn2} For all practiced purposes, we may assume log n < A(3,4) and hence ? (m,n) ? 3 m ? n ?The computing time of FJS is O(n) Additional 2n words of space for F and P are required.

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