Two Birthday Problem Modifications: Non-Uniform Case
نویسندگان
چکیده
منابع مشابه
A non-uniform birthday problem with applications to discrete logarithms
We consider a generalisation of the birthday problem that arises in the analysis of algorithms for certain variants of the discrete logarithm problem in groups. More precisely, we consider sampling coloured balls and placing them in urns, such that the distribution of assigning balls to urns depends on the colour of the ball. We determine the expected number of trials until two balls of differe...
متن کاملCounting Derangements, Non Bijective Functions and the Birthday Problem
The article provides counting derangements of finite sets and counting non bijective functions. We provide a recursive formula for the number of derangements of a finite set, together with an explicit formula involving the number e. We count the number of non-one-to-one functions between to finite sets and perform a computation to give explicitely a formalization of the birthday problem. The ar...
متن کاملA Generalized Birthday Problem
We study a k-dimensional generalization of the birthday problem: given k lists of n-bit values, find some way to choose one element from each list so that the resulting k values xor to zero. For k = 2, this is just the extremely well-known birthday problem, which has a square-root time algorithm with many applications in cryptography. In this paper, we show new algorithms for the case k > 2: we...
متن کاملThe Non-Uniform k-Center Problem
In this paper, we introduce and study the Non-Uniform k-Center (NUkC) problem. Given a finite metric space (X, d) and a collection of balls of radii {r1 ≥ · · · ≥ rk}, the NUkC problem is to find a placement of their centers on the metric space and find the minimum dilation α, such that the union of balls of radius α · ri around the ith center covers all the points in X . This problem naturally...
متن کاملThe Birthday Problem and Generalizations
The question that we began our comps process with, the Birthday Problem, is a relatively basic problem explored in elementary probability courses. To solve it, we find the probability that in a group of n people, two of them share the same birthday. The reason this problem is intriguing is that the probability values that we get as a result of our solution are much different that what one may e...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Research Bulletin of the National Technical University of Ukraine "Kyiv Polytechnic Institute"
سال: 2016
ISSN: 1810-0546
DOI: 10.20535/1810-0546.2016.4.76267