Abstract
Our interest is in paths between pairs of vertices that go through at least one of a subset of the vertices known as beer vertices. Such a path is called a beer path, and the beer distance between two vertices is the length of the shortest beer path. We show that we can represent unweighted interval graphs using 2n log n + O(n) + O(|B| log n) bits where |B| is the number of beer vertices. This data structure answers beer distance queries in O(logε n) time for any constant ε > 0 and shortest beer path queries in O(logε n + d) time, where d is the beer distance between the two nodes. We also show that proper interval graphs may be represented using 3n + o(n) bits to support beer distance queries in O(f(n) log n) time for any f(n) ∈ ω(1) and shortest beer path queries in O(d) time. All of these results also have time-space trade-offs. Lastly we show that the information theoretic lower bound for beer proper interval graphs is very close to the space of our structure, namely log(4 + 2 √3)n - o(n) (or about 2.9n) bits.
Original language | English |
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Title of host publication | 33rd International Symposium on Algorithms and Computation, ISAAC 2022 |
Editors | Sang Won Bae, Heejin Park |
Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |
ISBN (Electronic) | 9783959772587 |
DOIs | |
State | Published - 1 Dec 2022 |
Externally published | Yes |
Event | 33rd International Symposium on Algorithms and Computation, ISAAC 2022 - Virtual, Online, Korea, Republic of Duration: 19 Dec 2022 → 21 Dec 2022 |
Publication series
Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 248 |
ISSN (Print) | 1868-8969 |
Conference
Conference | 33rd International Symposium on Algorithms and Computation, ISAAC 2022 |
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Country/Territory | Korea, Republic of |
City | Virtual, Online |
Period | 19/12/22 → 21/12/22 |
Bibliographical note
Publisher Copyright:© Rathish Das, Meng He, Eitan Kondratovsky, J. Ian Munro, Anurag Murty Naredla, and Kaiyu Wu.
Keywords
- Beer Path
- Interval Graph