可变方向错位下的会合：固定单位距离的算法威力
Rendezvous under Variable Disorientation:The Algorithmic Power of Fixed Unit Distance
查看机构详情
- Notre Dame Seishin University（圣母清心女子大学）
- Hosei University（法政大学）
机构由 AI 辅助整理，请以论文原文为准。
浏览论文内容
中文总结 AI 辅助
本文研究弱假设下带灯机器人的确定性会合，提出周期距离类技术，利用固定单位距离实现更优颜色复杂度，并揭示度量稳定性与调度器原子性对可解性的影响。
中文摘要 AI 辅助
我们研究了在弱几何与弱同步假设下，两个带灯机器人的确定性会合问题。我们关注可变方向错位（VD），即每个机器人在每次“查看”时可能任意旋转、反射和缩放其局部坐标系，以及VD+固定单位距离（FUD），即每个机器人的局部单位距离保持固定。我们考虑单向可见性模型FSTA和FCOM，以及从能量受限的RSYNCH和R-RSYNCH到完全异步执行的调度器。在VD下，我们证明了SSYNCH下FSTA和ASYNCH下FCOM的与颜色无关的不可行性结果，并在RSYNCH和R-RSYNCH下建立了清晰的两色边界。在VD+FUD下，我们引入了周期距离类，将物理距离的乘法变化转化为可预测的循环相位偏移。该技术为RSYNCH和R-RSYNCH下的FSTA和FCOM（即使在非刚性移动下）产生了一个两色自稳定非L-会合算法。在刚性移动下，周期距离类进一步产生了SSYNCH下FSTA的最优三色非准自稳定算法、M-原子ASYNCH下的四色FSTA算法以及CM-原子ASYNCH下的四色FCOM算法。通过用两个额外颜色保护后一种相位机制并将其初始交换替换为被动初始化，我们在完全ASYNCH下获得了一个六色FCOM算法，将先前十二色的上界改进了一倍。这些结果表明，固定的局部度量可以作为持久的循环记忆，并阐明了度量稳定性、单向可见性和调度器原子性如何共同决定会合的可解性和颜色复杂度。
英文摘要
We study deterministic Rendezvous of two robots with lights under weak geometric and synchronization assumptions. Our focus is on Variable Disorientation (VD), where each robot may arbitrarily rotate, reflect, and rescale its local coordinate system at every \Look, and on VD+Fixed-Unit-Distance (FUD), where each robot's local unit distance remains fixed. We consider the one-sided visibility models FSTA and FCOM, and schedulers ranging from the energy-restricted RSYNCH and R-RSYNCH to fully asynchronous executions. Under VD, we prove color-independent impossibility results for FSTA under SSYNCH and for FCOM under ASYNCH, and establish sharp two-color boundaries under RSYNCH and R-RSYNCH. Under VD+FUD, we introduce periodic distance classes, which turn multiplicative changes of the physical distance into predictable cyclic phase shifts. This technique yields a two-color self-stabilizing non-$L$-Rendezvous algorithm for both FSTA and FCOM under RSYNCH and R-RSYNCH even with Non-Rigid movement. Under Rigid movement, periodic distance classes further yield an optimal three-color non-quasi-self-stabilizing algorithm for FSTA under SSYNCH, a four-color FSTA algorithm under $M$-atomic ASYNCH, and a four-color FCOM algorithm under CM-atomic ASYNCH. By guarding the latter phase mechanism with two additional colors and replacing its initial swap by passive initialization, we obtain a six-color FCOM algorithm under full ASYNCH, improving the previous twelve-color upper bound by a factor of two. These results show that a fixed local metric can serve as persistent cyclic memory, and clarify how metric stability, one-sided visibility, and scheduler atomicity jointly determine Rendezvous solvability and color complexity.
