Related papers: Avoiding patterns and making the best choice
We investigate pattern avoidance in alternating permutations and generalizations thereof. First, we study pattern avoidance in an alternating analogue of Young diagrams. In particular, we extend Babson-West's notion of shape-Wilf…
Bidding and acceptance strategies have a substantial impact on the outcome of negotiations in scenarios with linear additive and nonlinear utility functions. Over the years, it has become clear that there is no single best strategy for all…
We study a variation of the minority game. There are N agents. Each has to choose between one of two alternatives everyday, and there is reward to each member of the smaller group. The agents cannot communicate with each other, but try to…
We investigate permutations and involutions that avoid a pattern of length three and have a {\em unique} longest increasing subsequence.
Given permutations $\sigma \in S_k$ and $\pi \in S_n$ with $k<n$, the \emph{pattern matching} problem is to decide whether $\pi$ matches $\sigma$ as an order-isomorphic subsequence. We give a linear-time algorithm in case both $\pi$ and…
We study candidates' positioning when adjustments are possible in response to new information about voters' preferences. Re-positioning allows candidates to get closer to the median voter but is costly both financially and electorally. We…
Makespan minimization on identical machines is a fundamental problem in online scheduling. The goal is to assign a sequence of jobs to $m$ identical parallel machines so as to minimize the maximum completion time of any job. Already in the…
We study the longest increasing subsequence problem for random permutations avoiding the pattern $312$ and another pattern $\tau$ under the uniform probability distribution. We determine the exact and asymptotic formulas for the average…
In a delegation problem, a principal P with commitment power tries to pick one out of $n$ options. Each option is drawn independently from a known distribution. Instead of inspecting the options herself, P delegates the information…
In the past three decades, deductive games have become interesting from the algorithmic point of view. Deductive games are two players zero sum games of imperfect information. The first player, called "codemaker", chooses a secret code and…
When people pursue rewards in stochastic environments, they often match their choice frequencies to the observed target frequencies, even when this policy is demonstrably sub-optimal. We used a ``hide and seek'' task to evaluate this…
Suppose a set of requests arrives online: each request gives some value $v_i$ if accepted, but requires using some amount of each of $d$ resources. Our cost is a convex function of the vector of total utilization of these $d$ resources.…
Ensuring fairness in algorithmic ranking systems is a critical challenge with significant societal implications for hiring, recommendations, web search, and data management. Standard methods for aggregating multiple preference orders into a…
We study a variant of the secretary problem where candidates come from independent, not necessarily identical distributions known to us, and show that we can do at least as well as in the IID setting. This resolves a conjecture of…
We explore the question of how to learn an optimal search strategy within the example of a parking problem where parking opportunities arrive according to an unknown inhomogeneous Poisson process. The optimal policy is a threshold-type…
When recruiting job candidates, employers rarely observe their underlying skill level directly. Instead, they must administer a series of interviews and/or collate other noisy signals in order to estimate the worker's skill. Traditional…
We study the House Allocation problem (also known as the Assignment problem), i.e., the problem of allocating a set of objects among a set of agents, where each agent has ordinal preferences (possibly involving ties) over a subset of the…
`Twenty questions' is a guessing game played by two players: Bob thinks of an integer between $1$ and $n$, and Alice's goal is to recover it using a minimal number of Yes/No questions. Shannon's entropy has a natural interpretation in this…
What is the optimal order in which a researcher should submit their papers to journals of differing quality? I analyze a sequential search model without recall where the researcher's expected value from journal submission depends on the…
An open conjecture in pattern avoidance theory is that the distribution of the major index among 321-avoiding permutations is distributed unimodally. We construct a formula for this distribution, and in the case of 2 descents prove…