Related papers: Avoiding patterns and making the best choice
We show that, in a resource allocation problem, the ex ante aggregate utility of players with cumulative-prospect-theoretic preferences can be increased over deterministic allocations by implementing lotteries. We formulate an optimization…
We study a sequential decision-making model where a set of items is repeatedly matched to the same set of agents over multiple rounds. The objective is to determine a sequence of matchings that either maximizes the utility of the least…
Optimal stopping theory is a powerful tool for analyzing scenarios such as online auctions in which we generally require optimizing an objective function over the space of stopping rules for an allocation process under uncertainty. Perhaps…
A version of the secretary problem is considered. The ranks of items, whose values are independent, identically distributed random variables $X_1,X_2,...,X_n$ from a uniform distribution on $[0; 1]$, are observed sequentially by the grader.…
Prophet inequalities are a central object of study in optimal stopping theory. A gambler is sent values in an online fashion, sampled from an instance of independent distributions, in an adversarial, random or selected order, depending on…
A permutation $\pi$ is said to avoid a chain $(\sigma:\tau)$ of patterns if $\pi$ avoids $\sigma$ and $\pi^2$ avoids $\tau.$ In this paper, we define a notion of pattern avoidance for compositions of positive integers and use that idea to…
Chance-constrained problems involve stochastic components in the constraints which can be violated with a small probability. We investigate the impact of different types of chance constraints on the performance of iterative search…
We propose a non-autoregressive framework for the Travelling Salesman Problem where solutions emerge directly from learned permutations, without requiring explicit search. By applying a similarity transformation to Hamiltonian cycles, the…
This paper considers the ranking problem of candidates for a certain position based on ballot papers filled by voters. We suggest a ranking procedure of alternatives using cooperative game theory methods. For this, it is necessary to…
We study the selection of agents based on mutual nominations, a theoretical problem with many applications from committee selection to AI alignment. As agents both select and are selected, they may be incentivized to misrepresent their true…
Suppose a customer is faced with a sequence of fluctuating prices, such as for airfare or a product sold by a large online retailer. Given distributional information about what price they might face each day, how should they choose when to…
So far, the theory of equilibrium selection in the infinitely repeated prisoner's dilemma is insensitive to communication possibilities. To address this issue, we incorporate the assumption that communication reduces -- but does not…
A word $w=w_1w_2\cdots w_n$ is alternating if either $w_1<w_2>w_3<w_4>\cdots$ (when the word is up-down) or $w_1>w_2<w_3>w_4<\cdots$ (when the word is down-up). In this paper, we initiate the study of (pattern-avoiding) alternating words.…
Perfect sorting by reversals, a problem originating in computational genomics, is the process of sorting a signed permutation to either the identity or to the reversed identity permutation, by a sequence of reversals that do not break any…
We introduce the problem of ranking with slot constraints, which can be used to model a wide range of application problems -- from college admission with limited slots for different majors, to composing a stratified cohort of eligible…
In this paper, we propose how to use objective arguments grounded in statistical mechanics concepts in order to obtain a single number, obtained after aggregation, which would allow to rank "agents", "opinions", ..., all defined in a very…
We study the two-sided stable matching problem with one-sided uncertainty for two sets of agents A and B, with equal cardinality. Initially, the preference lists of the agents in A are given but the preferences of the agents in B are…
The hiring problem is studied for general strategies based only on the relative ranking of the candidates; this includes some well known strategies studied before such as hiring above the median. We give general limit theorems for the…
A special sorting operation called Context Directed Swap, and denoted \textbf{cds}, performs certain types of block interchanges on permutations. When a permutation is sortable by \textbf{cds}, then \textbf{cds} sorts it using the fewest…
Lookahead search is perhaps the most natural and widely used game playing strategy. Given the practical importance of the method, the aim of this paper is to provide a theoretical performance examination of lookahead search in a wide…