Tucker's lemma states that if we triangulate the unit disc centered at the origin and color the vertices with {1, 1,2, 2} in an antipodal way (if vertical bar z vertical bar = 1, then the sum of the colors of z and -z is zero), then there must be an edge For which the sum of the colors of its endpoints is zero. But how hard is it to find such all edge? We show Butt if the triangulation is exponentially large and the coloring is determined by a deterministic Turing-machine, then this problem is PPAD-complete which implies that there is not too much hope for a polynomial algorithm.

Published in:
Internet And Network Economics, Proceedings, 5929, 569-574
Presented at:
WINE 09, 5th International Workshop on Internet and Network Economics, Rome, ITALY, Dec 14-18, 2009
Year:
2009
Publisher:
Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa
ISBN:
978-3-642-10840-2
Keywords:
Laboratories: