Abstract
We study the problem of compact representation of graphs that have small bandwidth as well as graphs that have small treedepth. We present navigation oracles that support degree and adjacency queries in constant time and neighborhood queries in constant time per neighbor. For graphs of size n and bandwidth k, our oracle takes (k+⌈log2k⌉)n+o(kn) bits. We also show that (k−5k−4)n−O(k2) bits are required to encode such graphs. For graphs of size n and treedepth k, we present an oracle that takes (k+⌈logk⌉+2)n+o(kn) bits and complement it with lower bounds that show our oracle is compact for specific ranges of k. Our navigation oracles for both treedepth and treedepth parameters can be augmented, with additional n+o(n) bits, to support connectivity queries in constant time.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
