Generalized Balls into Bins

2026-08-21

AI Summary

研究通过贪婪算法解决广义球入箱问题，以优化分配策略并最小化箱子最终负载的期望值，适用于多种特定问题。

Abstract

Consider a set of bins and two-choice balls arriving by a Poisson process. We must allocate each incoming ball immediately to one of two incident bins. For a given function $f$ and every bin, we aim to bound the expectation of $f(L)$---where $L$ is the bin's final load---based on the arrival rate of balls incident to that bin. We call this problem Generalized Balls into Bins, capturing many problems as special cases including the original Balls into Bins by Azar et al. (1994) and Online Stochastic Matching by Feldman et al. (2009). We show that Greedy provides optimal amortized bounds for all convex and concave functions $f$. Further, we propose another algorithm that achieves non-trivial bounds without amortization. As an application, we design a competitive algorithm for a stochastic model of completion time minimization on unrelated machines.

Problem

• Balls into Bins
• Poisson process
• Load balancing
• Stochastic processes

Innovation

• Generalized Balls into Bins
• Greedy Algorithm
• Amortized Bounds
• Stochastic Completion Time Minimization