CSE4/586 (Spring 2009): Homework 7
Due by May 5 Tuesday, in class.
1.
(40 points)
Consider an undirected and connected (but not fullyconnected) graph of
n
nodes.
(In other words, the nodes are in a multihop network.)
Execution of nodes is
assumed to be synchronous— in each step/round, every node
j
executes its program action
(given below) with respect to one of its neighbors, that is chosen in a fixed cyclic ordering,
nxt
, of all of its neighbors.
Program
Unison
var
x.j
:
int
r.j
: any value from the set
{
k

k
is a neighbor of
j
}
assign
x.j, r.j
:=
min
(
x.j, x.
(
r.j
)) + 1
, nxt.
(
r.j
)
1. Show that this program satisfies the property of Unison: Starting from any
unison
state
, i.e., one where all
x
variables have equal values, the value of each
x
variable is
incremented by one in every following step/round of the system. (This implies that all
states following a unison state are also unison states.)
2. Prove the stabilization of the program. Hint: show that “true leads to unison states”.
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 Spring '09
 qwerty
 Integers, Harshad number, 71, proposal number, Jim Waldo

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