<s>
Rocha	B-Operating_System
–	I-Operating_System
Thatte	I-Operating_System
algorithm	I-Operating_System
is	O
a	O
distributed	B-Operating_System
algorithm	I-Operating_System
in	O
graph	O
theory	O
for	O
detecting	O
cycles	O
on	O
large-scale	O
directed	O
graphs	O
based	O
on	O
the	O
bulk	B-Application
synchronous	I-Application
message	O
passing	O
abstraction	O
.	O
</s>
<s>
The	O
Rocha	B-Operating_System
–	I-Operating_System
Thatte	I-Operating_System
algorithm	I-Operating_System
is	O
a	O
general	O
algorithm	O
for	O
detecting	O
cycles	O
in	O
a	O
directed	O
graph	O
by	O
message	O
passing	O
among	O
its	O
vertices	O
,	O
based	O
on	O
the	O
bulk	B-Application
synchronous	I-Application
message	O
passing	O
abstraction	O
.	O
</s>
<s>
The	O
bulk	B-Application
synchronous	I-Application
parallel	I-Application
model	O
consists	O
of	O
a	O
sequence	O
of	O
iterations	O
,	O
in	O
each	O
of	O
which	O
a	O
vertex	O
can	O
receive	O
messages	O
sent	O
by	O
other	O
vertices	O
in	O
the	O
previous	O
iteration	O
,	O
and	O
send	O
messages	O
to	O
other	O
vertices	O
.	O
</s>
<s>
Simulations	O
show	O
that	O
the	O
Rocha-Thatte	B-Operating_System
algorithm	I-Operating_System
has	O
a	O
smaller	O
communication	O
overhead	O
than	O
a	O
distributed	O
version	O
of	O
depth-first	B-Algorithm
search	I-Algorithm
,	O
regarding	O
both	O
the	O
number	O
of	O
messages	O
and	O
the	O
total	O
number	O
of	O
bits	O
sent	O
.	O
</s>
<s>
Specifically	O
,	O
the	O
distributed	O
version	O
of	O
DFS	B-Algorithm
may	O
require	O
up	O
to	O
one	O
order	O
of	O
magnitude	O
more	O
messages	O
exchanged	O
than	O
the	O
Rocha-Thatte	B-Operating_System
algorithm	I-Operating_System
.	O
</s>
