Succinct Data Structures for Bounded Degree/Chromatic Number Interval Graphs

Meng He, J. Ian Munro, Kaiyu Wu

Abstract: An interval graph is the intersection graph of intervals on the real line. We consider the problem of constructing space efficient data structures for two subclasses of interval graphs: those with maximum degree σ1 and those with chromatic number at most σ2.We show that both bounded degree and bounded chromatic number interval graphs have a tight lower bound of n lg σi − o(n lg σi) bits (i = 1, 2). This improves the lower bound of Chakraborty and Jo from $\frac{1}{6}n\lg {\sigma _i} - O(n)$. For bounded chromatic number interval graphs, we give the first succinct data structure occupying n lg σ2 + O(n) bits that supports navigational operations and distance queries in O(σ2 lgn) time. To match Chakraborty and Jo’s time complexity of O(lg lg σ2), which uses (σ2 − 1)n+O(n) bits, we use 2nlgσ2 +O(n) bits instead.