动态冲突解决机制
Dynamic Contention Resolution Schemes
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- University of Haifa（海法大学）
- Washington University in St. Louis（圣路易斯华盛顿大学）
- Rutgers University（罗格斯大学）
- Carnegie Mellon University（卡内基梅隆大学）
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中文总结 AI 辅助
本文提出动态冲突解决机制（DCRS），一种用于完全动态打包问题的低追索舍入范式，可组合约束并产生具有竞争力的追索算法，首次为非二分匹配和动态背包问题给出非平凡追索界。
中文摘要 AI 辅助
我们为完全动态环境下的打包问题引入了一种低追索舍入范式，称之为动态冲突解决机制（DCRSs）。这些是（在线）冲突解决机制（或（O）CRSs）在低追索动态优化中的动态类比，并提供了多种益处。与其离线和在线对应物类似，针对不同约束的DCRSs可以组合起来，以获得这些约束交集上的DCRSs。此外，结合Bhattacharya、Buchbinder、Levin和Saranurak [FOCS 2023]的正体追逐框架，DCRSs为具有次模目标的完全动态打包问题提供了具有竞争力的追索算法：这些算法对于任何输入序列，所产生的追索本身相对于该序列的最佳可能追索具有竞争力。我们证明了对于拟阵约束，存在Ω(1)-平衡且O(log rank)-追索的DCRSs，而对于匹配和背包约束，存在Ω(1)-平衡/O(1)-追索的DCRSs。特别地，这些结果为完全动态背包问题首次给出了非平凡的追索界，也为非二分匹配问题首次给出了具有竞争力的追索算法，并且这两者都适用于单调次模目标。除了我们的具体结果之外，我们将DCRS框架视为在动态优化背景下机械化近似算法的松弛与舍入范式的一个原则性步骤。
英文摘要
We introduce a low-recourse rounding paradigm for packing problems in fully dynamic settings, which we name Dynamic Contention Resolution Schemes (DCRSs). These are dynamic analogs of (Online) Contention Resolution Schemes (or (O)CRSs) for low-recourse dynamic optimization and offer a variety of benefits. Similarly to their offline and online counterparts, DCRSs for different constraints can be combined to obtain DCRSs for the constraints' intersection. Furthermore, together with the Positive Body Chasing framework of Bhattacharya, Buchbinder, Levin, and Saranurak [FOCS 2023], DCRSs imply competitive recourse algorithms for fully dynamic packing problems with submodular objectives: these are algorithms that, for any input sequence, incur recourse that is itself competitive with the best possible recourse for that sequence. We show the existence of $Ω(1)$-balanced and $O(\log \mathrm{rank})$-recourse DCRSs for matroid constraints, and $Ω(1)$-balanced/$O(1)$-recourse DCRSs for matching and knapsack constraints. In particular, these yield the first non-trivial recourse bound for fully dynamic knapsack, as well as the first competitive-recourse algorithm for non-bipartite matching, and both of these apply even to monotone submodular objectives. Beyond our particular results, we view the DCRS framework as a principled step towards mechanizing the relax-and-round paradigm of approximation algorithms in the context of dynamic optimization.
