具有最大延迟的子可加服务成本在线覆盖
Online Covering with Maximum Delay under Subadditive Service Costs
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中文总结 AI 辅助
该论文研究具有最大等待时间的在线覆盖问题，证明单调子可加性足以达到最优竞争比，提出确定性ρ+1和随机1/(1-e^{-1/ρ})的算法，并给出精确批处理的常数2和e/(e-1)，通过加权顶点覆盖展示与子模性的分离。
中文摘要 AI 辅助
我们研究在线覆盖问题，其中每次即时服务需支付其购买成本并允许一个最大等待时间，且不影响未来的请求。对于静态可实现服务，单调子可加性足以获得最优竞争比，而无需子模性。一个具有实现因子ρ的归一化单调子可加下界预言机，在对抗性对手下，确定性算法达到ρ+1的竞争比，随机算法达到1/(1-e^{-1/ρ})的竞争比。精确批处理优化给出最优常数2和e/(e-1)。随机算法使用一个基于种子无关虚拟高度轨迹的全局阈值，其活动时间是离线最优值的下界。加权顶点覆盖在三边二分路径上与子模性严格分离，通过最小割和LP舍入实现多项式时间批处理实现。离线连续批处理范式也将静态近似保证转移到离线问题。
英文摘要
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 $ρ$ yields ratios $ρ+1$ deterministically and $1/(1-e^{-1/ρ})$ 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.
发表机构
- Southern University of Science and Technology（南方科技大学）
机构由 AI 辅助整理，请以论文原文为准。
