Average-case lower bounds for the plurality problem

Given a set of n elements, each of which is colored one of c 2 colors, we must determine an element of the plurality (most frequently occurring) color by pairwise equal/unequal color comparisons of elements. We derive lower bounds for the expected number of color comparisons when the cn colorings are equally probable. We prove a general lower bound of c 3n - O( n) for c 2; we prove the stronger particular bounds of 7 6 n-O( n) for c = 3, 54 35 n-O( n) for c = 4, 607 315n-O( n) for c = 5, 1592 693 n - O( n) for c = 6, 7985 3003n - O( n) for c = 7, and 19402 6435 n - O( n) for c = 8. Key words. Algorithm analysis, plurality problem AMS(MOS) subject classifications. 68Q25, 68P10, 68Q20, 68M15

• Type: Journal
• Year: 2008
• Where: TALG
• Authors: Laurent Alonso, Edward M. Reingold
• Keywords: Color Comparisons, General Lower Bound, Lower Bound, TALG 2008