![](bg6.png)
agent dependency graph and then to use this feed-
back vertex set V
0
to create a sufficient set of coor-
dination arcs by adequately blocking connections in
the corresponding task sets of agents occurring in V
0
.
This blocking can be realized by adding arcs from all
source to all sink tasks occurring in the task sets.
So the FVS-algorithm essentially consists of the
following steps:
1. Given a coordination instance h{T
i
}
n
i=1
, ≺i, cre-
ate the associated agent dependency graph G
A
=
hV
A
, E
A
i;
2. Find an approximation
6
of a minimum directed
feedback vertex set F ⊂ V
A
of G
A
. ;
3. For every v
A
i
∈ F, for every t ∈ Out(T
i
) (source
task) and for every t
0
∈ In(T
i
) (sink task), add the
coordination constraint t ≺
∗
i
t
0
thereby blocking
any cycle passing through tasks belonging to A
i
.
It can be easily shown that in most cases this algo-
rithm will outperform the existing depth partitioning
algorithm (Steenhuisen et al., 2008)
7
.
5 CONCLUSIONS AND FUTURE
WORK
This paper identified a new subclass of coordina-
tion problems called intra-free coordination instances
which have a relevance to model production and dis-
tribution planning problems in particular and supply
chain planning in general. We have shown that the
(decision version of the) plan coordination problem
for this subproblem is NP-complete, instead of the Σ
P
2
complexity of the general coordination problem. We
also proposed a specialized approximation technique
to design a ‘good’ set of coordination constraints in
polynomial time.
As part of our future research, first of all we are in-
vestigating better heuristics for producing subset min-
imal coordination sets e.g., as we have discussed in
the previous section, and we would like to refine the
theoretical performance comparison analysis based
upon them.
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6
We can use any known approximation algorithm for
this problem.
7
Due to space limitations, we omit the performance
analysis in this paper.
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