Problem
Research questions and friction points this paper is trying to address.
Online Matching
Convex Bipartite Graphs
Resource Allocation
Competitive Ratio
Online Matching in Convex Bipartite Graphs
🤖 AI Summary
研究在线匹配问题在凸二分图中的应用，提出Flip算法，通过随机选择最早或最晚可行分配来提高竞争比至2/3。
📝 Abstract
Online resource-allocation systems, like outpatient scheduling and spectrum allocation, often assign sequentially arriving requests to an ordered pool of scarce resources, where each request accepts a contiguous interval of feasible options. We study the resulting online matching problem on convex bipartite graphs under irrevocable decisions and adversarial arrivals. We first show that convexity alone does not improve the classic worst-case guarantee of 1-1/e, achieved by Ranking. We then consider the uniform-length model, in which every online request has exactly d consecutive offline neighbors. We propose Flip, which uses one random bit to commit ex-ante to either earliest-feasible assignment or latest-feasible assignment. Although either natural deterministic policy can waste capacity and be asymptotically only 1/2-competitive, we show that their randomized mixture is 2/3-competitive. This guarantee is tight for Flip and remains valid against a semi-adaptive adversary that observes the selected policy before choosing the arrival order. We also prove that no randomized online algorithm can achieve a competitive ratio strictly larger than 3/4 in the uniform-length model.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Flip algorithm
convex bipartite graphs
online matching
randomized mixture
competitive ratio
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