Skip to main content Accessibility help
×
Hostname: page-component-848d4c4894-p2v8j Total loading time: 0.001 Render date: 2024-05-19T23:59:31.357Z Has data issue: false hasContentIssue false

4 - Bitvectors

Published online by Cambridge University Press:  05 September 2016

Gonzalo Navarro
Affiliation:
Universidad de Chile
Get access
Type
Chapter
Information
Compact Data Structures
A Practical Approach
, pp. 64 - 102
Publisher: Cambridge University Press
Print publication year: 2016

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Beame, P. and Fich, F. E. (2002). Optimal bounds for the predecessor problem and related problems. Journal of Computer and System Sciences, 65(1), 38–72.Google Scholar
Belazzougui, D., Botelho, F. C., and Dietzfelbinger, M. (2009). Hash, displace, and compress. In 17th Annual European Symposium on Algorithms (ESA), LNCS 5757, pages 682–693.Google Scholar
Belazzougui, D., Boldi, P., Pagh, R., and Vigna, S. (2011). Theory and practice of monotone minimal perfect hashing. ACM Journal of Experimental Algorithmics, 16(3), article 2.Google Scholar
Beskers, K. and Fischer, J. (2014). High-order entropy compressed bit vectors with rank/select. Algorithms, 7, 608–620.Google Scholar
Botelho, F. C., Pagh, R., and Ziviani, N. (2013). Practical perfect hashing in nearly optimal space. Information Systems, 38(1), 108–131.Google Scholar
Brodnik, A. and Munro, J. I. (1999). Membership in constant time and almost-minimum space. SIAM Journal on Computing, 28(5), 1627–1640.Google Scholar
Carter, L. and Wegman, M. N. (1979). Universal classes of hash functions. Journal of Computer and System Sciences, 18(2), 143–154.Google Scholar
Chazelle, B., Kilian, J., Rubinfeld, R., and Tal, A. (2004). The Bloomier filter: an efficient data structure for static support lookup tables. In Proc. 15th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 30–39.Google Scholar
Clark, D. R. (1996). Compact PAT Trees. Ph.D. thesis, University of Waterloo, Canada.
Claude, F. and Navarro, G. (2008). Practical rank/select queries over arbitrary sequences. In Proc. 15th International Symposium on String Processing and Information Retrieval (SPIRE), LNCS 5280, pages 176–187.Google Scholar
Cormen, T. H., Leiserson, C. E., Rivest, R. L., and Stein, C. (2009). Introduction to Algorithms. MIT Press, 3rd edition.
Davisson, L. D. (1966). Comments on ‘Sequence time coding for data compression.’ Proceedings of the IEEE (Corresp.), 54, 2010.Google Scholar
Delpratt, O., Rahman, N., and Raman, R. (2006). Engineering the LOUDS succinct tree representation. In Proc. 5th International Workshop on Experimental Algorithms (WEA), LNCS 4007, pages 134–145.Google Scholar
Dementiev, R., Kettner, L., Mehnert, J., and Sanders, P. (2004). Engineering a sorted list data structure for 32 bit key. In Proc. 6thWorkshop on Algorithm Engineering and Experiments (ALENEX), pages 142–151.Google Scholar
Elias, P. (1974). Efficient storage and retrieval by content and address of static files. Journal of the ACM, 21, 246–260.Google Scholar
Fano, R. (1971). On the number of bits required to implement an associative memory. Memo 61, Computer Structures Group, Project MAC, Massachusetts.
Ferragina, P. and Venturini, R. (2007). A simple storage scheme for strings achieving entropy bounds. Theoretical Computer Science, 371(1), 115–121.Google Scholar
Foschini, L., Grossi, R., Gupta, A., and Vitter, J. S. (2006). When indexing equals compression: Experiments with compressing suffix arrays and applications. ACM Transactions on Algorithms, 2(4), 611–639.Google Scholar
Fredman, M. L., Komlós, J., and Szemerédi, E. (1984). Storing a sparse table with O(1) worst case access time. Journal of the ACM, 31(3), 538–544.Google Scholar
Gog, S. and Petri, M. (2014). Optimized succinct data structures for massive data. Software Practice and Experience, 44(11), 1287–1314.Google Scholar
Golynski, A. (2007). Optimal lower bounds for rank and select indexes. Theoretical Computer Science, 387(3), 348–359.Google Scholar
Golynski, A., Grossi, R., Gupta, A., Raman, R., and Rao, S. S. (2007). On the size of succinct indices. In Proc. 15th Annual European Symposium on Algorithms (ESA), LNCS 4698, pages 371–382.Google Scholar
Golynski, A., Orlandi, A., Raman, R., and Rao, S. S. (2014). Optimal indexes for sparse bit vectors. Algorithmica, 69(4), 906–924.Google Scholar
González, R., Grabowski, S., Mäkinen, V., and Navarro, G. (2005). Practical implementation of rank and select queries. In Proc. Posters of 4th Workshop on Efficient and Experimental Algorithms (WEA), pages 27–38.Google Scholar
Grossi, R., Orlandi, A., Raman, R., and Rao, S. S. (2009). More haste, less waste: Lowering the redundancy in fully indexable dictionaries. In Proc. 26th International Symposium on Theoretical Aspects of Computer Science (STACS), LIPIcs 3, pages 517–528.Google Scholar
Gupta, A., Hon, W.-K., Shah, R., and Vitter, J. S. (2007). Compressed data structures: Dictionaries and data-aware measures. Theoretical Computer Science, 387(3), 313–331.Google Scholar
Hon, W.-K., Sadakane, K., and Sung, W.-K. (2011). Succinct data structures for searchable partial sums with optimal worst-case performance. Theoretical Computer Science, 412(39), 5176–5186.Google Scholar
Jacobson, G. (1989). Space-efficient static trees and graphs. In Proc. 30th IEEE Symposium on Foundations of Computer Science (FOCS), pages 549–554.Google Scholar
Kärkkäinen, J., Kempa, D., and Puglisi, S. J. (2014). Hybrid compression of bitvectors for the FMindex. In Proc. 24th Data Compression Conference (DCC), pages 302–311.Google Scholar
Knuth, D. E. (2009). The Art of Computer Programming, volume 4: Fascicle 1: Bitwise Tricks & Techniques; Binary Decision Diagrams. Addison-Wesley Professional.
Mehlhorn, K. and Näher, S. (1990). Bounded ordered dictionaries in O(log logN) time and O(n) space. Information Processing Letters, 35(4), 183–189.Google Scholar
Motwani, R. and Raghavan, P. (1995). Randomized Algorithms. Cambridge University Press.
Nash, N. and Gregg, D. (2008). Comparing integer data structures for 32 and 64 bit keys. In Proc. 10th Workshop on Algorithm Engineering and Experiments (ALENEX), LNCS 5038, pages 28–42.Google Scholar
Navarro, G. and Providel, E. (2012). Fast, small, simple rank/select on bitmaps. In Proc. 11th International Symposium on Experimental Algorithms (SEA), LNCS 7276, pages 295–306.Google Scholar
Okanohara, D. and Sadakane, K. (2007). Practical entropy-compressed rank/select dictionary. In Proc. 9th Workshop on Algorithm Engineering and Experiments (ALENEX), pages 60–70.Google Scholar
Pagh, R. (2001). Low redundancy in static dictionaries with constant query time. SIAM Journal of Computing, 31(2), 353–363.Google Scholar
Pătraşcu, M. (2008). Succincter. In Proc. 49th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pages 305–313.Google Scholar
Pătraşcu, M. and Viola, E. (2010). Cell-probe lower bounds for succinct partial sums. In Proc. 21st Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 117–122.Google Scholar
Raman, R., Raman, V., and Rao, S. S. (2007). Succinct indexable dictionaries with applications to encoding k-ary trees, prefix sums and multisets. ACM Transactions on Algorithms, 3(4), article 43.Google Scholar
Vigna, S. (2008). Broadword implementation of rank/select queries. In Proc. 7th International Workshop on Experimental Algorithms (WEA), LNCS 5038, pages 154–168.Google Scholar
Zhou, D., Andersen, D. G., and Kaminsky, M. (2013). Space-efficient, high-performance rank and select structures on uncompressed bit sequences. In Proc. 12th International Symposium on Experimental Algorithms (SEA), LNCS 7933, pages 151–163.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • Bitvectors
  • Gonzalo Navarro, Universidad de Chile
  • Book: Compact Data Structures
  • Online publication: 05 September 2016
  • Chapter DOI: https://doi.org/10.1017/CBO9781316588284.005
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • Bitvectors
  • Gonzalo Navarro, Universidad de Chile
  • Book: Compact Data Structures
  • Online publication: 05 September 2016
  • Chapter DOI: https://doi.org/10.1017/CBO9781316588284.005
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Bitvectors
  • Gonzalo Navarro, Universidad de Chile
  • Book: Compact Data Structures
  • Online publication: 05 September 2016
  • Chapter DOI: https://doi.org/10.1017/CBO9781316588284.005
Available formats
×