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Summary: Systems & Control Letters 7 (1986) 329-332
North-Holland
July 1986
An optimal strategy for a conflict resolution
problem
V. ANANTHARAM and P. VARAIYA
Deportment of Electric01 Engineering ond Computer Science
and Electronics Research Laboratory,
University of California, Berkeley, CA 94720, USA
Received 25 October 1985
Abstrocr: Relevant to the design of multiple access protocols is
the problem of finding the largest of N i.i.d. numbers X,, .. ., X,
uniformly distributed over (0, l] using the minimum number of
questions of the following type. We pick a set A(1) c [0, l] and
ask which X, E A(1). Depending on the response, we pick
another subset A(2) and ask which Xi E A(2), and so on, until
we identify the largest Xi. It is shown that the optimum
sequence of questions must be of the type A(k) = (o(k), 11;
the best sequence (o(k)) can then be determined by dynamic
programming following the work of Arrow. Pesotchinsky and
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