Data-Driven Service Composition - Business and Scientific Workflows - page 54

Qð P C Þ is an ordered list

of transitions, and each transition is an output transition of a conflict
place, that is,

P C Þ is a finite set of n -tuples. Each tuple h in Qð

Qð P C Þ¼fð t 1 m 1 ; t 2 m 2 ; ... ; t nm n Þ j m i 2f 1 ; 2 ; ... ; k i g; i 2f 1 ; 2 ; ... ; n g g

Each h ¼ð t 1 q 1 ; t 2 q 2 ; ... ; t nq n Þ2Qð P C Þ is a selection tuple (or h

tuple) with respect to conflict place set P C .
For h

¼ð t 1 q 1 ; t 2 q 2 ; ... ; t nq n Þ2Qð P C Þ , we define

Y h ð

p i Þ¼ t iq i

For example, in Figure 3.8, P C ¼f p 1 g , then

Qð P C Þ¼fð t 1 Þ; ð t 2 Þ; ð t 31 Þ; ð t 32 Þg

If we define h 1 ¼ð t 31 Þ; h 2 ¼ð t 32 Þ2Qð P C Þ , then

Y h 1 ð Y h 2 ð

p 1 Þ¼ t 31 ; p 1 Þ¼ t 32

j ,or
t i and t j belong to the same group of a mediation transition. For
example, in Figure 3.8, t 31

relation among transitions, t i

t j if i ¼

We also define the

t 32 . We use it later in the following
decomposition algorithm such that mediation transitions are treated as
one group.

Algorithm 3.1. (Decomposition Algorithm)

Input:

N R ¼ð P ; T ; F Þ ; P C ¼f p 1 ; p 2 ; ... ; p n g P

h ¼ð t 1 q 1 ; t 2 q 2 ; ... ; t nq n Þ2Qð P C Þ

Output:

R i ¼ð P i ; T i ; F i Þ