Abstract:

For the only known universal best choice algorithm for partially ordered sets with known cardinality and unknown order (proposed by J. Preater) we improve the estimation of the lower bound of its chance of success from the hitherto known constant 1/8 to 1/4. We also show that this result is the best possible for this algorithm, i.e., the 1/4 bound cannot be further improved. The result is based on my joint paper with Nicholas Georgiou, Malgorzata Kuchta, and Jaroslaw Niemiec: "On a universal best choice algorithm for partially ordered sets" (to appear in Random Structures and Algorithms).