论文标题
通过广度优先/选择简洁的树木的距离隔离图
Distance Oracles for Interval Graphs via Breadth-First Rank/Select in Succinct Trees
论文作者
论文摘要
我们使用新型的序数树结构（未加权）间隔图和相关类别的类别的第一个简洁的距离牙文，用于序列树的新型简洁数据结构，该结构支持预订（即深度优先）等级和级别级别等级（广度 - 优先）在恒定时间内的节点等级。我们用于间隔图的距离门还支持导航查询 - 测试邻接，计算节点度，邻域和最短路径 - 都在最佳时间内。我们的技术还产生最佳的距离甲骨文，以用于适当的间隔图（单位间隔图）和圆形ARC图。我们的树数据结构支持以前工作中不同方法提供的所有操作，以及从级别等级进行映射，并在（之后）在级别段落中（之后）一个给定节点之前的最后一个（第一个）内部节点，所有节点均保持恒定时间。
We present the first succinct distance oracles for (unweighted) interval graphs and related classes of graphs, using a novel succinct data structure for ordinal trees that supports the mapping between preorder (i.e., depth-first) ranks and level-order (breadth-first) ranks of nodes in constant time. Our distance oracles for interval graphs also support navigation queries -- testing adjacency, computing node degrees, neighborhoods, and shortest paths -- all in optimal time. Our technique also yields optimal distance oracles for proper interval graphs (unit-interval graphs) and circular-arc graphs. Our tree data structure supports all operations provided by different approaches in previous work, as well as mapping to and from level-order ranks and retrieving the last (first) internal node before (after) a given node in a level-order traversal, all in constant time.
