Weighted games of best choice
- MathematicsSIAM J. Discret. Math.
A general class of permutation statistics is introduced that always produces games of best choice whose optimal strategy is positional and produces a new proof of a foundational result from the literature on the secretary problem.
Finding the Second-Best Candidate under the Mallows Model
- Mathematics, Computer ScienceTheoretical Computer Science
Secretary Problem with Possible Errors in Observation
This article proposes modeling doubts of decision maker by considering a modification of the secretary problem that assumes that the decision maker can not observe the relative ranks in a proper way and calculates the optimal strategy and the value of the problem.
SHOWING 1-10 OF 26 REFERENCES
Recognizing the Maximum of a Sequence
Abstract The classical dowry, secretary, or beauty contest problem is extended in several directions. In trying to find sequentially the maximum of a random sequence of fixed length, the chooser can…
Secretary Problems with Non-Uniform Arrival Order
- Computer Science, MathematicsSTOC
This work initiates an investigation into relaxations of the random-ordering hypothesis in online algorithms, by focusing on the secretary problem and asking what performance guarantees one can prove under relaxed assumptions, and proves that Θ(log log n) is the minimum entropy of any permutation distribution that permits constant probability of correct selection in the secretaries problem with $n$ elements.
Online auctions and generalized secretary problems
- Computer ScienceSECO
This work presents generalized secretary problems as a framework for online auctions, and presents surprisingly strong constant factor guarantees on the expected value of solutions obtained by online algorithms.
Who Solved the Secretary Problem
The object of this article is to give a fresh view of the origins of the problem, touching upon Cayley and Kepler, and review of the field (listing the subfields of recent interest), partly serious (to answer the question posed in the title), and partly entertainment.
A GENERALIZATION OF THE CLASSICAL SECRETARY PROBLEM: DEPENDENT ARRIVAL SEQUENCES
This paper presents new methods for selecting the best population value under the classical secretary problem sequential selection rules. Unlike the classical case, the possible population arrival…
Structure of random 312‐avoiding permutations
- Mathematics, Computer ScienceRandom Struct. Algorithms
The exact formulas for the probability that the ith element of a random permutation is a specific value less than i are derived, and for joint probabilities of two such events are obtained.
Longest Increasing Subsequences in Pattern-Restricted Permutations
- MathematicsElectron. J. Comb.
The limiting distributions for pattern-restricted permutations in which the pattern is any one of the six patterns of length 3 are found, and it is shown that the (132)-avoiding case is identical to the distribution of heights of ordered trees, and the (321) case has interesting connections with a well known theorem of Erd\H os-Szekeres.
What is known about Robbins' Problem?
Let X 1 , X 2 , ..., X n be independent, identically distributed random variables, uniform on [0,1]. We observe the X k sequentially and must stop on exactly one of them. No recollection of the…
Generating trees and the Catalan and Schröder numbers
- MathematicsDiscret. Math.