In this work we introduce and study a pursuit-evasion game in which the search is performed by heterogeneous entities. We incorporate heterogeneity into the classical edge search problem by considering edge-labeled graphs: once a search strategy initially assigns labels to the searchers, each searcher can be only present on an edge of its own label. We prove that this problem is not monotone even for trees and we give instances in which the number of recontamination events is asymptotically quadratic in the tree size. Other negative results regard the NP-completeness of the monotone, and NP-hardness of an arbitrary (i.e., non-monotone) heterogeneous search in trees. These properties show that this problem behaves very differently from the classical edge search. On the other hand, if all edges of a particular label form a (connected) subtree of the input tree, then we show that optimal heterogeneous search strategy can be computed efficiently.

在这项工作中，我们介绍和研究一种追逃游戏，其中搜索是由异构实体执行的。我们通过考虑边缘标记图将异质性纳入经典边缘搜索问题：一旦搜索策略最初为搜索者分配了标签，每个搜索者只能出现在其自己的标签的边缘上。我们证明即使对于树木，这个问题也不是单调的，并且我们给出了实例，其中再污染事件的数量在树的大小上渐近二次方。其他负面结果涉及单调的NP完整性和树木中任意（即非单调）异构搜索的NP硬度。这些属性表明，此问题的行为与经典边缘搜索非常不同。另一方面，