scholarly journals Secretary Problem: Graphs, Matroids and Greedoids

2021 ◽  
Vol 2 (4) ◽  
Author(s):  
Wojciech Kordecki
Keyword(s):  
Cloud Computing ◽  
Secretary Problem ◽  
Binary Trees ◽  
Special Cases

AbstractIn the paper, the generalisation of the well-known “secretary problem” is considered. The aim of the paper is to give a generalised model in such a way that the chosen set of the possible best k elements have to be independent of all previously rejected elements. The independence is formulated using the theory of greedoids and in their special cases—matroids and antimatroids. Examples of some special cases of greedoids (uniform, graphical matroids and binary trees) are considered. Applications in cloud computing are discussed.

Recognizing the maximum of a random sequence based on relative rank with backward solicitation

1974 ◽  
Vol 11 (03) ◽  
pp. 504-512 ◽  
Author(s):  
Mark C. K. Yang
Keyword(s):  
General Formula ◽  
Optimal Stopping ◽  
Random Sequence ◽  
Geometric Probability ◽  
Secretary Problem ◽  
Stopping Rules ◽  
Relative Rank ◽  
Special Cases ◽  
Optimal Stopping Rules

The classical secretary problem is generalized to admit stochastically successful procurement of previous interviewees, but each has a certain probability of refusing the offer. A general formula for solving this problem is obtained. Two special cases: constant probability of refusing and geometric probability of refusing are discussed in detail. The optimal stopping rules in these two cases turn out to be simple.

scholarly journals Compare the ratio of symmetric polynomials of odds to one and stop

2017 ◽  
Vol 54 (1) ◽  
pp. 12-22
Author(s):  
Tomomi Matsui ◽  
Katsunori Ano
Keyword(s):  
Lower Bound ◽  
Optimal Stopping ◽  
Optimization Technique ◽  
Secretary Problem ◽  
Symmetric Polynomials ◽  
Threshold Strategy ◽  
Optimal Stopping Rule ◽  
Special Cases ◽  
Unified View ◽  
Special Case

AbstractIn this paper we deal with an optimal stopping problem whose objective is to maximize the probability of selecting k out of the last ℓ successes, given a sequence of independent Bernoulli trials of length N, where k and ℓ are predetermined integers satisfying 1≤k≤ℓ<N. This problem includes some odds problems as special cases, e.g. Bruss’ odds problem, Bruss and Paindaveine’s problem of selecting the last ℓ successes, and Tamaki’s multiplicative odds problem for stopping at any of the last m successes. We show that an optimal stopping rule is obtained by a threshold strategy. We also present the tight lower bound and an asymptotic lower bound for the probability of a win. Interestingly, our asymptotic lower bound is attained by using a variation of the well-known secretary problem, which is a special case of the odds problem. Our approach is based on the application of Newton’s inequalities and optimization technique, which gives a unified view to the previous works.

Recognizing the maximum of a random sequence based on relative rank with backward solicitation

1974 ◽  
Vol 11 (3) ◽  
pp. 504-512 ◽  
Author(s):  
Mark C. K. Yang
Keyword(s):  
General Formula ◽  
Optimal Stopping ◽  
Random Sequence ◽  
Geometric Probability ◽  
Secretary Problem ◽  
Stopping Rules ◽  
Relative Rank ◽  
Special Cases ◽  
Optimal Stopping Rules

The classical secretary problem is generalized to admit stochastically successful procurement of previous interviewees, but each has a certain probability of refusing the offer. A general formula for solving this problem is obtained. Two special cases: constant probability of refusing and geometric probability of refusing are discussed in detail. The optimal stopping rules in these two cases turn out to be simple.

scholarly journals Secretary Problem with Possible Errors in Observation

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1639
Author(s):  
Marek Skarupski
Keyword(s):  
Decision Maker ◽  
Empirical Result ◽  
Optimal Strategy ◽  
Secretary Problem ◽  
Theoretical Studies ◽  
Choice Problem ◽  
Second Best ◽  
Optimal Rule ◽  
Best Choice Problem ◽  
Special Cases

The classical secretary problem models a situation in which the decision maker can select or reject in the sequential observation objects numbered by the relative ranks. In theoretical studies, it is known that the strategy is to reject the first 37% of objects and select the next relative best one. However, an empirical result for the problem is that people do not apply the optimal rule. In this article, we propose modeling doubts of decision maker by considering a modification of the secretary problem. We assume that the decision maker can not observe the relative ranks in a proper way. We calculate the optimal strategy in such a problem and the value of the problem. In special cases, we also combine this problem with the no-information best choice problem and a no-information second-best choice problem.

Optimizing a single uncertain selection by recall of observations

1994 ◽  
Vol 31 (3) ◽  
pp. 660-672 ◽  
Author(s):  
Ted Sweet
Keyword(s):  
Optimal Strategies ◽  
Secretary Problem ◽  
Optimal Procedure ◽  
Special Cases ◽  
Probability Of Success

This paper considers a variation of the classical secretary problem; this variation allows for the interviewer to make an offer to previously interviewed applicants and for the applicant to reject an offer. In this version, the process ends after any offer is made. Two special cases are considered, where the optimal procedure and its probability of success are given for each. Furthermore, the problem is discussed in general and conditions for optimal strategies are given.

A Ratio Inequality for Binary Trees and the Best Secretary

2002 ◽  
Vol 11 (2) ◽  
pp. 149-161 ◽  
Author(s):  
GRZEGORZ KUBICKI ◽  
JENŐ LEHEL ◽  
MICHAŁ MORAYNE
Keyword(s):  
Optimal Stopping ◽  
Binary Tree ◽  
Stopping Time ◽  
Secretary Problem ◽  
Hasse Diagram ◽  
Binary Trees ◽  
Complete Binary Tree ◽  
Maximum Element ◽  
Optimal Stopping Time ◽  
Natural Behaviour

Let Tn be the complete binary tree of height n considered as the Hasse diagram of a poset with its root 1n as the maximum element. Define A(n; T) = [mid ]{S ⊆ Tn : 1n ∈ S, S ≅ T}[mid ], and B(n; T) = [mid ]{S ⊆ Tn : 1n ∉ S, S ≅ T}[mid ]. In this note we prove that for any fixed n and rooted binary trees T1, T2 such that T2 contains a subposet isomorphic to T1. We conjecture that the ratio A/B also increases with T for arbitrary trees. These inequalities imply natural behaviour of the optimal stopping time in a poset extension of the secretary problem.

Optimizing a single uncertain selection by recall of observations

1994 ◽  
Vol 31 (03) ◽  
pp. 660-672
Author(s):  
Ted Sweet
Keyword(s):  
Optimal Strategies ◽  
Secretary Problem ◽  
Optimal Procedure ◽  
Special Cases ◽  
Probability Of Success

This paper considers a variation of the classical secretary problem; this variation allows for the interviewer to make an offer to previously interviewed applicants and for the applicant to reject an offer. In this version, the process ends after any offer is made. Two special cases are considered, where the optimal procedure and its probability of success are given for each. Furthermore, the problem is discussed in general and conditions for optimal strategies are given.

Electron Beam Damage of Biomolecules Assessed by Energy Loss Spectroscopy

1978 ◽  
Vol 36 (3) ◽  
pp. 61-69
Author(s):  
M. Isaacson ◽  
M.L. Collins ◽  
M. Listvan
Keyword(s):  
Electron Microscopy ◽  
Radiation Damage ◽  
Structural Integrity ◽  
Analytical Electron Microscopy ◽  
High Dose ◽  
Dose Rates ◽  
Special Cases ◽  
Analytical Electron ◽  
Atom Migration ◽  
Beam Damage

Over the past five years it has become evident that radiation damage provides the fundamental limit to the study of blomolecular structure by electron microscopy. In some special cases structural determinations at very low doses can be achieved through superposition techniques to study periodic (Unwin & Henderson, 1975) and nonperiodic (Saxton & Frank, 1977) specimens. In addition, protection methods such as glucose embedding (Unwin & Henderson, 1975) and maintenance of specimen hydration at low temperatures (Taylor & Glaeser, 1976) have also shown promise. Despite these successes, the basic nature of radiation damage in the electron microscope is far from clear. In general we cannot predict exactly how different structures will behave during electron Irradiation at high dose rates. Moreover, with the rapid rise of analytical electron microscopy over the last few years, nvicroscopists are becoming concerned with questions of compositional as well as structural integrity. It is important to measure changes in elemental composition arising from atom migration in or loss from the specimen as a result of electron bombardment.

Decoration technique and surface physics

1978 ◽  
Vol 36 (1) ◽  
pp. 436-437 ◽  
Author(s):  
H. Bethge
Keyword(s):  
Diffusion Path ◽  
Special Importance ◽  
Surface Physics ◽  
Step Structure ◽  
Initial Stage ◽  
Special Cases ◽  
Atomic Surface ◽  
The Mean ◽  
Bulk Structure ◽  
Decoration Technique

Besides the atomic surface structure, diverging in special cases with respect to the bulk structure, the real structure of a surface Is determined by the step structure. Using the decoration technique /1/ it is possible to image step structures having step heights down to a single lattice plane distance electron-microscopically. For a number of problems the knowledge of the monatomic step structures is important, because numerous problems of surface physics are directly connected with processes taking place at these steps, e.g. crystal growth or evaporation, sorption and nucleatlon as initial stage of overgrowth of thin films.To demonstrate the decoration technique by means of evaporation of heavy metals Fig. 1 from our former investigations shows the monatomic step structure of an evaporated NaCI crystal. of special Importance Is the detection of the movement of steps during the growth or evaporation of a crystal. From the velocity of a step fundamental quantities for the molecular processes can be determined, e.g. the mean free diffusion path of molecules.

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