Related papers: Weber's optimal stopping problem and generalizatio…
In the classical secretary problem, one attempts to find the maximum of an unknown and unlearnable distribution through sequential search. In many real-world searches, however, distributions are not entirely unknown and can be learned…
We consider a generalization of the secretary problem where contracts are temporary, and for a fixed duration. This models online hiring of temporary employees, or online auctions for re-usable resources. The problem is related to the…
We study a learning-augmented variant of the secretary problem, recently introduced by Fujii and Yoshida (2023), in which the decision-maker has access to machine-learned predictions of candidate values. The central challenge is to balance…
Constraint satisfaction problems (CSPs) consist of a set of variables taking values from some finite domain and a set of local constraints on these variables. The objective is to find an assignment to the variables that maximizes the…
We study variants of the secretary problem, where $N$, the number of candidates, is a random variable, and the decision maker wants to maximize the probability of success -- picking the largest number among the $N$ candidates -- using only…
In learning-augmented online algorithms, predictions are usually valued for what they say: a value estimate, a solution, or an algorithmic recommendation. This paper shows that predictions can also be valuable solely due to their arrival…
The decision-maker (DM) sequentially evaluates up to N of different, rankable options. DM must select exactly the best one at the moment of its appearance. In the process of searching, DM finds out with each applicant whether she is the…
Robbins' problem of optimal stopping asks one to minimise the expected {\it rank} of observation chosen by some nonanticipating stopping rule. We settle a conjecture regarding the {\it value} of the stopped variable under the rule optimal…
The secretary problem is probably the purest model of decision making under uncertainty. In this paper we ask which advice can we give the algorithm to improve its success probability? We propose a general model that unifies a broad range…
We study the submodular secretary problem with a cardinality constraint. In this problem, $n$ candidates for secretaries appear sequentially in random order. At the arrival of each candidate, a decision maker must irrevocably decide whether…
Optimization problems involving complex variables, when solved, are typically transformed into real variables, often at the expense of convergence rate and interpretability. This paper introduces a novel formalism for a prominent problem in…
In the prophet secretary problem, $n$ values are drawn independently from known distributions, and presented in a uniformly random order. A decision-maker must accept or reject each value when it is presented, and may accept at most $k$…
We study parameterized Constraint Satisfaction Problem for infinite constraint languages. The parameters that we study are weight of the satisfying assignment, number of constraints, maximum number of occurrences of a variable in the…
In the last two decades the study of random instances of constraint satisfaction problems (CSPs) has flourished across several disciplines, including computer science, mathematics and physics. The diversity of the developed methods, on the…
Many online problems are studied in stochastic settings for which inputs are samples from a known distribution, given in advance, or from an unknown distribution. Such distributions model both beyond-worst-case inputs and, when given,…
This article considers a problem arising from a two-player game based on the classical secretary problem. First, Player 1 selects one object from a sequence as in the secretary problem. All of the other objects are then presented to Player…
We solve the secretary problem in the case that the ranked items arrive in a statistically biased order rather than in uniformly random order. The bias is given by a Mallows distribution with parameter $q\in(0,1)$, so that higher ranked…
We investigate rules which allow variable elimination in binary CSP (constraint satisfaction problem) instances while conserving satisfiability. We study variable-elimination rules based on the language of forbidden patterns enriched with…
In this paper we consider two variants of the Secretary problem: The Best-or-Worst and the Postdoc problems. We extend previous work by considering that the number of objects is not known and follows either a discrete Uniform distribution…
In this paper we study a generalized version of the Weber problem of finding a point that minimizes the sum of its distances to a finite number of given points. In our setting these distances may be $cut$ $off$ at a given value $C > 0$, and…