ﻻ يوجد ملخص باللغة العربية
Suppose we sequentially put $n$ balls into $n$ bins. If we put each ball into a random bin then the heaviest bin will contain ${sim}log n/loglog n$ balls with high probability. However, Azar, Broder, Karlin and Upfal [SIAM J. Comput. 29 (1999) 180--200] showed that if each time we choose two bins at random and put the ball in the least loaded bin among the two, then the heaviest bin will contain only ${sim}loglog n$ balls with high probability. How much memory do we need to implement this scheme? We need roughly $logloglog n$ bits per bin, and $nlogloglog n$ bits in total. Let us assume now that we have limited amount of memory. For each ball, we are given two random bins and we have to put the ball into one of them. Our goal is to minimize the load of the heaviest bin. We prove that if we have $n^{1-delta}$ bits then the heaviest bin will contain at least $Omega(deltalog n/loglog n)$ balls with high probability. The bound is tight in the communication complexity model.
Grimmett and McDiarmid suggested a simple heuristic for finding stable sets in random graphs. They showed that the heuristic finds a stable set of size $simlog_2 n$ (with high probability) on a $G(n, 1/2)$ random graph. We determine the asymptotic di
Spectral algorithms, such as principal component analysis and spectral clustering, typically require careful data transformations to be effective: upon observing a matrix $A$, one may look at the spectrum of $psi(A)$ for a properly chosen $psi$. The
The Load-Balanced Router architecture has received a lot of attention because it does not require centralized scheduling at the internal switch fabrics. In this paper we reexamine the architecture, motivated by its potential to turn off multiple comp
In recent years much effort has been concentrated towards achieving polynomial time lower bounds on algorithms for solving various well-known problems. A useful technique for showing such lower bounds is to prove them conditionally based on well-stud
This paper initiates the study of the classic balanced graph partitioning problem from an online perspective: Given an arbitrary sequence of pairwise communication requests between $n$ nodes, with patterns that may change over time, the objective is