We consider online content recommendation with implicit feedback through pairwise comparisons, formalized as the so-called dueling bandit problem. We study the dueling bandit problem in the Condorcet winner setting, and consider two notions of regret: the more well-studied strong regret, which is 0 only when both arms pulled are the Condorcet winner; and the less well-studied weak regret, which...

In this paper we consider the problem of computing the weak visibility polygon of any query line segment pq (or WVP(pq)) inside a given polygon P . Our first non-trivial algorithm runs in simple polygons and needs O(n log n) time and O(n) space in the preprocessing phase to report WVP(pq) of any query line segment pq in time O(log n + |WVP(pq)|). We also give an algorithm to compute the weak vi...

Given a set P of n points in Rd and > 0, we consider the problem of constructing weak -nets for P . We show the following: pick a random sample Q of size O(1/ log (1/ )) from P . Then, with constant probability, a weak -net of P can be constructed from only the points of Q. This shows that weak -nets in Rd can be computed from a subset of P of size O(1/ log(1/ )) with only the constant of propo...

Abstract We study the weak convergence order of two Euler-type discretizations log-Heston model where we use symmetrization and absorption, respectively, to prevent discretization underlying CIR process from becoming negative. If Feller index $\nu $ satisfies $\nu>1$, establish 1 $, while for \leq 1$, obtain -\epsilon $\epsilon>0$ arbitrarily small. illustrate our theoretical find...

OF THE DISSERTATION Algorithms and LP-Duality Based Lower Bounds in Ad-hoc Radio Networks by Rohan Jude Fernandes Dissertation Director: Mart́ın Farach-Colton An Ad-hoc Radio Network consists of nodes with no knowledge of its neighbors and knowledge of its own ID and n, the size of the network. In this thesis, we present algorithms and lower bounds related to ad-hoc network initialization. Senso...

We show the existence of weak ε-nets of size O (1/ε log log (1/ε)) for point sets and axisparallel boxes in R, for d ≥ 4. Our analysis uses a non-trivial variant of the recent technique of Aronov et al. [2] that yields (strong) ε-nets, whose size have the above asymptotic bound, for d = 2, 3.

This paper considers the computation of matrix chain products of the form M1 M2 Mn?1. The order in which the matrices are multiplied aaects the number of operations. The best sequential algorithm for computing an optimal order of matrix multiplication runs in O(n log n) time while the best known parallel NC algorithm runs in O(log 2 n) time using n 6 = log 6 n processors. This paper presents th...

§1. Conjectures Let V be a variety over C and let B = ∑ biBi be an effective Q-Weil divisor on V such that bi ≤ 1 for any i. Such a pair (V,B) will be called a log variety. It is said to be log terminal if it has only weak log terminal singularities in the sense of [KMM]. In this case, the Q-bundle KV + B is called the log canonical bundle of (V,B) and will be denoted by K(V,B). A Q-bundle L on...

A partition (C1, C2, ..., Cq) ofG = (V,E) into clusters of strong (respectively, weak) diameter d, such that the supergraph obtained by contracting each Ci is l-colorable is called a strong (resp., weak) (d, l)network-decomposition. Network-decompositions were introduced in a seminal paper by Awerbuch, Goldberg, Luby and Plotkin in 1989. Awerbuch et al. showed that strong (exp{O(√logn log logn)...