We consider labeling schemes for trees, supporting various relationships between nodes at small distance. For instance, we show that given a tree T and an integer k we can assign labels to each node of T such that given the label of two nodes we can decide, from these two labels alone, if the distance between v and w is at most k and if so compute it. For trees with n nodes and k ≥ 2, we give a lower bound on the maximum label length of log n + Ω(log log n) bits, and for constant k, we give an upper bound of log n + O(log log n). Bounds for ancestor, sibling, connectivity and bi- and triconnectivity labeling schemes are also presented.
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机译：我们考虑了树的标记方案，以支持小距离节点之间的各种关系。例如，我们显示给定一棵树 T 和一个整数 k ，我们可以为 T 的每个节点分配标签，从而给定标签为我们可以单独从这两个标签中确定两个节点， v 和 w 之间的距离是否最多为 k ，如果可以，则进行计算。对于具有 n 个节点且 k ≥2的树，我们给出log n +Ω（log log < I> n ）位，对于常数 k ，我们给出日志 n + O （log log < I> n ）。还介绍了祖先，同级，连通性以及双连通性和三连通性标记方案的界限。
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