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We study certain self-interacting walks on the set of integers, that choose to jump to the right or to the left randomly but influenced by the number of times they have previously jumped along the edges in the finite neighbourhood of their…
We consider a budget-constrained bandit problem where each arm pull incurs a random cost, and yields a random reward in return. The objective is to maximize the total expected reward under a budget constraint on the total cost. The model is…
With the goal to provide absolute lower bounds for the best possible running times that can be achieved by $(1+\lambda)$-type search heuristics on common benchmark problems, we recently suggested a dynamic programming approach that computes…
In this paper we present a method for obtaining tail-bounds for random variables satisfying certain probabilistic recurrences that arise in the analysis of randomized parallel divide and conquer algorithms. In such algorithms, some…
The best algorithm so far for solving Simple Stochastic Games is Ludwig's randomized algorithm which works in expected $2^{O(\sqrt{n})}$ time. We first give a simpler iterative variant of this algorithm, using Bland's rule from the simplex…
The ellipsoid fitting conjecture of Saunderson, Chandrasekaran, Parrilo and Willsky considers the maximum number $n$ random Gaussian points in $\mathbb{R}^d$, such that with high probability, there exists an origin-symmetric ellipsoid…
Although animal locations gained via GPS, etc. are typically observed on a discrete time scale, movement models formulated in continuous time are preferable in order to avoid the struggles experienced in discrete time when faced with…
In this paper we report on an experimental test of Bertrand's question on the probability to find a random chord drawn inside a unit-radius circle with length greater than $\sqrt{3}$. In an experiment performed by tossing straws onto a…
We study a natural random walk on the $n \times n$ upper triangular matrices, with entries in $\mathbb{Z}/m \mathbb{Z}$, generated by steps which add or subtract a uniformly random row to the row above. We show that the mixing time of this…
Given n elements with nonnegative integer weights w1,..., wn and an integer capacity C, we consider the counting version of the classic knapsack problem: find the number of distinct subsets whose weights add up to at most the given…
We introduce a fun problem that can be considered as a variant of the classic birthday problem, the Bottleneck Birthday Problem (BBP). It is stated as: what is the maximum number of people we have to choose so that no day of the year has…
We consider trap models on Z^d, namely continuous time Markov jump process on Z^d with embedded chain given by a generic discrete time random walk, and whose mean waiting time at x is given by tau_x, with tau = (tau_x, x in Z^d) a family of…
Consider a set $P$ of $n$ points picked uniformly and independently from $[0,1]^d$ for a constant dimension $d$ -- such a point set is extremely well behaved in many aspects. For example, for a fixed $r \in [0,1]$, we prove a new…
Mandelbrot multiplicative cascades provide a construction of a dynamical system on a set of probability measures defined by inequalities on moments. To be more specific, beyond the first iteration, the trajectories take values in the set of…
Proposed in 1937, the Collatz conjecture has remained in the spotlight for mathematicians and computer scientists alike due to its simple proposal, yet intractable proof. In this paper, we propose several novel theorems, corollaries, and…
Hierarchical Clustering is a popular unsupervised machine learning method with decades of history and numerous applications. We initiate the study of differentially private approximation algorithms for hierarchical clustering under the…
Consider n unit intervals, say [1,2], [3,4], ..., [2n-1,2n]. Identify their endpoints in pairs at random, with all (2n-1)!! = (2n-1) (2n-3) ... 3 1 pairings being equally likely. The result is a collection of cycles of various lengths, and…
The Pandora's Box problem models the search for the best alternative when evaluation is costly. In the simplest variant, a decision maker is presented with $n$ boxes, each associated with a cost of inspection and a hidden random reward. The…
Randomized rounding is a standard method, based on the probabilistic method, for designing combinatorial approximation algorithms. In Raghavan's seminal paper introducing the method (1988), he writes: "The time taken to solve the linear…
In this paper, we present a local information theoretic approach to explicitly learn probabilistic clustering of a discrete random variable. Our formulation yields a convex maximization problem for which it is NP-hard to find the global…