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In this paper, we propose a deterministic algorithm that approximates the optimal path cover on weighted undirected graphs. Based on the 1/2-Approximation Path Cover Algorithm by Moran et al., we add a procedure to remove the redundant…
We describe optimal robust algorithms for finding a triangle and the unweighted girth in a unit disk graph, as well as finding a triangle in a transmission graph.In the robust setting, the input is not given as a set of sites in the plane,…
We offer some theorems, mainly of finiteness, for certain patterns in elliptical billiards, related to periodic trajectories. For instance, if two players hit a ball at a given position and with directions forming a fixed angle in…
Given a mixture between two populations of coins, "positive" coins that each have -- unknown and potentially different -- bias $\geq\frac{1}{2}+\Delta$ and "negative" coins with bias $\leq\frac{1}{2}-\Delta$, we consider the task of…
This thesis studies the graph alignment problem, the noisy version of the graph isomorphism problem, which aims to find a matching between the nodes of two graphs which preserves most of the edges. Focusing on the planted version where the…
Complex geometries can be easily treated using the well-known full-way and half-way bounce-back rules. However, the accuracy of the full-way bounce-back rule is one order lower than the half-way bounce-back rule. Moreover, when the walls…
We examine the dynamics of cylinders that are grooved to form N teeth for rolling motion down an inclined plane. The grooved cylinders are experimentally found to reach a terminal velocity. This result can be explained by the inclusion of…
The problem of counting tilings of a plane region using specified tiles can often be recast as the problem of counting (perfect) matchings of some subgraph of an Aztec diamond graph A_n, or more generally calculating the sum of the weights…
Numerically simulating deformations in thin elastic sheets is a challenging problem in computational mechanics due to destabilizing compressive stresses that result in wrinkling. Determining the location, structure, and evolution of…
Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…
We consider the problem of uniformity testing of Lipschitz continuous distributions with bounded support. The alternative hypothesis is a composite set of Lipschitz continuous distributions that are at least $\varepsilon$ away in $\ell_1$…
We study a new modification of the Arrival problem, which allows for nodes that exhibit random as well as controlled behaviour, in addition to switching nodes. We study the computational complexity of these extensions, building on existing…
The cryptographic protocol of coin tossing consists of two parties, Alice and Bob, that do not trust each other, but want to generate a random bit. If the parties use a classical communication channel and have unlimited computational…
We introduce in this study an algorithm for the imaging of faults and of slip fields on those faults. The physics of this problem are modeled using the equations of linear elasticity. We define a regularized functional to be minimized for…
We analyse the equilibrium pile-up configurations of infinite periodic walls of edge dislocations which are forced against an impenetrable obstacle by a constant applied shear stress. Numerically generated density distributions exhibit two…
Can a probabilistic gambler get arbitrarily rich when all deterministic gamblers fail? We study this problem in the context of algorithmic randomness, introducing a new notion -- almost everywhere computable randomness. A binary sequence…
This paper considers the computational hardness of computing expected outcomes and deciding (universal) (positive) almost-sure termination of probabilistic programs. It is shown that computing lower and upper bounds of expected outcomes is…
We consider chance-constrained binary knapsack problems, where the weights of items are independent random variables with the means and standard deviations known. The chance constraint can be reformulated as a second-order cone constraint…
Penney's game is a two player zero-sum game in which each player chooses a three-flip pattern of heads and tails and the winner is the player whose pattern occurs first in repeated tosses of a fair coin. Because the players choose…
In this note we consider the maximization of the expected terminal wealth for the setup of quadratic transaction costs. First, we provide a very simple probabilistic solution to the problem. Although the problem was largely studied, as far…