Section: New Results
Algorithms and combinatorics
Participant : Laurent Alonso.
Bounds for Cops and Robber Pursuit
We prove that the robber can evade (that is, stay at least unit distance from)
at least 
cops patroling an n×n continuous
square region, that a robber can always evade a single cop patroling a square
with side length 4 or larger, and that a single cop on patrol can always
capture the robber in a square with side length smaller than
(with E.M. Reingold, submitted to J. of Computational Geometry
Theory and Applications).
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 have to 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
for c2 ; we prove the stronger particular
bounds of 
for c = 3 , 
for c = 4 , 
for c = 5 , 
for c = 6 , 
for c = 7 , and
for c = 8 (with E.M. Reigold, [11] ).
