Only recently progress has been made in obtaining o(log(rank))-competitive algorithms for the matroid secretary problem. More precisely, Chakraborty and Lachish (2012) presented a O( √ log(rank))-competitive procedure, and Lachish (2014) later presented a O(log log(rank))competitive algorithm. Both these algorithms and their analyses are very involved, which is also reflected in the extremely h...

Land use/land cover change has been attracting increasing attention in the field of global environmental change research because of its role in the social and ecological environment. To explore the ecological risk characteristics of land use change in the Poyang Lake Eco-economic Zone of China, an eco-risk index was established in this study by the combination of a landscape disturbance index w...

We treat a version of the multiple-choice secretary problem called the multiplechoice duration problem, in which the objective is to maximize the time of possession of relatively best objects. It is shown that, for the m–choice duration problem, there exists a sequence (s1, s2, . . . , sm) of critical numbers such that, whenever there remain k choices yet to be made, then the optimal strategy i...

In the classical secretary problem, n objects from an ordered set arrive in random order, and one has to accept k of them so that the nal decision about each object is made only on the basis of its rank relative to the ones already seen. Variants of the problem depend on the goal: either maximize the probability of accepting the best k objects, or minimize the expectation of the sum of the rank...

The classical secretary problem has been generalized over the years into several directions. In this paper we confine our interest to those generalizations which have to do with the more general problem of stopping on a last observation of a specific kind. We follow Dendievel [10], [11], (where a bibliography can be found) who studies several types of such problems, mainly initiated by Bruss [3...

The menu-dependent nature of regret-minimization creates subtleties in applying regret-minimization to dynamic decision problems. Firstly, it is not clear whether forgone opportunities should be included in the menu. We explain commonly observed behavioral patterns as minimizing regret when forgone opportunities are present, and also show how the treatment of forgone opportunities affects behav...

The classical secretary problem investigates the question of how to hire the best secretary from n candidates who come in a uniformly random order. In this work we investigate a parallel generalizations of this problem introduced by Feldman and Tennenholtz [14]. We call it shared Q-queue J-choice K-best secretary problem. In this problem, n candidates are evenly distributed into Q queues, and i...

In the Prophet Secretary problem, samples from a known set of probability distributions arrive one by one in a uniformly random order, and an algorithm must irrevocably pick one of the samples as soon as it arrives. The goal is to maximize the expected value of the sample picked relative to the expected maximum of the distributions. This is one of the most simple and fundamental problems in onl...

The J-choice K-best secretary problem, also known as the (J, K)-secretary problem, is a generalization of the classical secretary problem. An algorithm for the (J, K)-secretary problem is allowed to make J choices and the payoff to be maximized is the expected number of items chosen among the K best items. Previous works analyzed the case when the total number n of items is finite, and consider...

In the classical secretary problem, the objective is to select the candidate of maximum value among a set of n candidates arriving one by one. The value of the candidates come from an unknown distribution and is revealed at the time the candidate arrives, at which point an irrevocable decision on whether to select the candidate must be made. The well-known solution to this problem, due to Dynki...