竞争分配策略下的集体搜索-捕获问题
Collective search-and-capture under competing assignment policies
AI总结：
该研究构建集体搜索-捕获格点模型，发现完成时间与游走者持续性呈非单调关系，且最大基数匹配分配策略相比贪心策略可大幅缩短捕获时间，其调控作用强于游走者持续性。
AI中文摘要：
我们研究了一个主动搜索-捕获的最小格点模型，其中持续随机游走者通过有限范围的互斥分配规则，定位并不可逆地捕获静止目标。我们测量了集体完成时间$T_c$与游走者重定向率$α$和搜索半径$R$的函数关系。$T_c(α)$的依赖关系是非单调的，在中等持续性处存在最小值，且该最小值的深度随$R$增大而减小。捕获动力学表明，$T_c$并非典型捕获时间，而是由捕获过程极端的后期尾部主导，大部分目标的捕获时间要早得多；该尾部主要由自由探索阶段而非最终的定向接近阶段控制。随后我们将基线单轮分配规则与级联重分配、候选图上的最大基数匹配（maximum-cardinality matching）进行了对比。两种贪心策略（单轮与级联）在$R$极小时表现一致，而最大基数匹配在中等$R$下已能实现显著加速：在大$R$下优化匹配可将$T_c$降低数倍，在中等$R$下降幅超过一个数量级。因此，在这个存在消耗耦合的集体搜索问题中，分配策略对捕获时间的控制作用强于游走者的持续性。
英文摘要：
We study a minimal lattice model of active search-and-capture in which persistent random walkers locate and irreversibly capture immobile targets through a finite-range, mutually exclusive assignment rule. We measure the collective completion time $T_c$ as a function of the walkers' reorientation rate $α$ and the search radius $R$. The dependence $T_c(α)$ is non-monotonic, with a minimum at intermediate persistence whose depth decreases as $R$ grows. Capture kinetics show that $T_c$ is not a typical capture time but is governed by the extreme, late-time tail of the capture process, while the bulk of targets are captured much earlier; this tail is controlled mainly by the free-exploration phase rather than by the final directed approach. We then compare the baseline single-round assignment rule with cascading reassignment and with maximum-cardinality matching on a candidate graph. The two greedy policies (single-round and cascading) agree at very small $R$, whereas maximum-cardinality matching already produces a strong speedup at moderate $R$: improved matching reduces $T_c$ by factors of several at large $R$, and by more than an order of magnitude at moderate $R$. Thus, in this collective, depletion-coupled search problem, the assignment policy can control the capture time more strongly than the walkers' persistence.
