Online Covering with Maximum Delay under Subadditive Service Costs

2026-09-26

AI Summary

本文研究带最大延迟和次可加成本的在线覆盖问题，利用下界预言机与全局阈值随机化算法实现最优竞争比。

Abstract

We study online covering in which each instantaneous service pays its purchase cost and one maximum waiting time, with no effect on future requests. For static realizable services, monotone subadditivity suffices for optimal competitive ratios; submodularity is unnecessary. A normalized monotone subadditive lower-bound oracle with realization factor $\rho$ yields ratios $\rho+1$ deterministically and $1/(1-e^{-1/\rho})$ randomly against an oblivious adversary. Exact batch optimization gives the optimal constants $2$ and $e/(e-1)$. The randomized algorithm uses one global threshold on a seed-independent virtual-height trajectory, whose active time is a lower bound on the offline optimum. Weighted vertex cover gives a strict separation from submodularity on a three-edge bipartite path, with polynomial-time batch implementations through min-cut and LP rounding. An offline consecutive-batch normal form also transfers static approximation guarantees to the offline problem.

Problem

• online covering
• maximum delay
• subadditive service costs
• competitive ratio
• submodularity

Innovation

• online covering
• subadditive service costs
• competitive ratio
• randomized algorithm
• weighted vertex cover