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External-Memory Priority Queues with Optimal Insertions

Authors Gerth Stølting Brodal , Michael T. Goodrich , John Iacono , Jared Lo , Ulrich Meyer , Victor Pagan , Nodari Sitchinava , Rolf Svenning

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Subject Classification

ACM Subject Classification
  • Theory of computation → Data structures design and analysis
Keywords
  • priority queues
  • external memory
  • cache aware
  • amortized complexity

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Abstract

We present an external-memory priority queue structure supporting Insert and DeleteMin with amortized 𝒪(1) and 𝒪(lg N) comparisons, respectively, and amortized 𝒪(1/B) and 𝒪(1/B log_{M/B} N/B) I/Os, respectively. Here, M is the size of the internal memory, B is the block size of I/Os between internal and external memory, and N is the number of elements in the priority queue just before an operation is performed. Previous external-memory priority queues required amortized 𝒪(lg N) comparisons and 𝒪(1/B log_{M/B} N/B) I/Os for both Insert and DeleteMin. The construction requires the minimal assumption M ≥ 2B.

Cite As Get BibTex

Gerth Stølting Brodal, Michael T. Goodrich, John Iacono, Jared Lo, Ulrich Meyer, Victor Pagan, Nodari Sitchinava, and Rolf Svenning. External-Memory Priority Queues with Optimal Insertions. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 5:1-5:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ESA.2025.5

Author Details

Gerth Stølting Brodal
  • Aarhus University, Denmark
Michael T. Goodrich
  • University of California, Irvine, CA, USA
John Iacono
  • Université libre de Bruxelles, Belgium
Jared Lo
  • University of Hawai'i at Mānoa, Honolulu, HI, USA
Ulrich Meyer
  • Goethe University Frankfurt am Main, Germany
Victor Pagan
  • University of Hawai'i at Mānoa, Honolulu, HI, USA
Nodari Sitchinava
  • University of Hawai'i at Mānoa, Honolulu, HI, USA
Rolf Svenning
  • Aarhus University, Denmark

Funding

Work initiated while attending the Third AlgoPARC Workshop on Parallel Algorithms and Data Structures at the University of Hawaii at Manoa, in part supported by the National Science Foundation under Grant No. 2452276.
  • Brodal, Gerth Stølting: Supported by Independent Research Fund Denmark, grant 9131-00113B.
  • Goodrich, Michael T.: Supported by NSF grant 2212129.
  • Iacono, John: Research supported by the Fonds de la Recherche Scientifique - FNRS.
  • Lo, Jared: Supported by NSF grant 2432018.
  • Meyer, Ulrich: Supported by Deutsche Forschungsgemeinschaft (DFG) - ME 2088/5-2 (FOR 2975 - Algorithms, Dynamics, and Information Flow in Networks).
  • Pagan, Victor: Supported by NSF grant 2432018.
  • Sitchinava, Nodari: Supported by NSF grant 2432018.
  • Svenning, Rolf: Supported by Independent Research Fund Denmark, grant 9131-00113B.

References

  1. Alok Aggarwal and Jeffrey Scott Vitter. The input/output complexity of sorting and related problems. Communications of the ACM, 31(9):1116-1127, 1988. URL: https://doi.org/10.1145/48529.48535.
  2. David P. Dobkin andJ. Ian Munro. Optimal time minimal space selection algorithms. Journal of the ACM, 28(3):454-461, 1981. URL: https://doi.org/10.1145/322261.322264.
  3. Lars Arge. The buffer tree: A technique for designing batched external data structures. Algorithmica, 37(1):1-24, 2003. URL: https://doi.org/10.1007/S00453-003-1021-X.
  4. Lars Arge, Michael A. Bender, Erik D. Demaine, Bryan Holland-Minkley, and J. Ian Munro. An optimal cache-oblivious priority queue and its application to graph algorithms. SIAM Journal of Computing, 36(6):1672-1695, 2007. URL: https://doi.org/10.1137/S0097539703428324.
  5. Manuel Blum, Robert W. Floyd, Vaughan R. Pratt, Ronald L. Rivest, and Robert Endre Tarjan. Time bounds for selection. Journal of Computer and System Sciences, 7(4):448-461, 1973. URL: https://doi.org/10.1016/S0022-0000(73)80033-9.
  6. Klaus Brengel, Andreas Crauser, Paolo Ferragina, and Ulrich Meyer. An experimental study of priority queues in external memory. In Jeffrey Scott Vitter and Christos D. Zaroliagis, editors, Algorithm Engineering, 3rd International Workshop, WAE '99, London, UK, July 19-21, 1999, Proceedings, volume 1668 of Lecture Notes in Computer Science, pages 346-360. Springer, 1999. URL: https://doi.org/10.1007/3-540-48318-7_27.
  7. Gerth Stølting Brodal. A survey on priority queues. In Andrej Brodnik, Alejandro López-Ortiz, Venkatesh Raman, and Alfredo Viola, editors, Space-Efficient Data Structures, Streams, and Algorithms - Papers in Honor of J. Ian Munro on the Occasion of His 66th Birthday, volume 8066 of Lecture Notes in Computer Science, pages 150-163. Springer, 2013. URL: https://doi.org/10.1007/978-3-642-40273-9_11.
  8. Gerth Stølting Brodal and Rolf Fagerberg. Cache oblivious distribution sweeping. In Peter Widmayer, Francisco Triguero Ruiz, Rafael Morales Bueno, Matthew Hennessy, Stephan J. Eidenbenz, and Ricardo Conejo, editors, Automata, Languages and Programming, 29th International Colloquium, ICALP 2002, Malaga, Spain, July 8-13, 2002, Proceedings, volume 2380 of Lecture Notes in Computer Science, pages 426-438. Springer, 2002. URL: https://doi.org/10.1007/3-540-45465-9_37.
  9. Gerth Stølting Brodal and Rolf Fagerberg. Funnel heap - A cache oblivious priority queue. In Prosenjit Bose and Pat Morin, editors, Algorithms and Computation, 13th International Symposium, ISAAC 2002 Vancouver, BC, Canada, November 21-23, 2002, Proceedings, volume 2518 of Lecture Notes in Computer Science, pages 219-228. Springer, 2002. URL: https://doi.org/10.1007/3-540-36136-7_20.
  10. Gerth Stølting Brodal and Rolf Fagerberg. On the limits of cache-obliviousness. In Lawrence L. Larmore and Michel X. Goemans, editors, Proceedings of the 35th Annual ACM Symposium on Theory of Computing, June 9-11, 2003, San Diego, CA, USA, pages 307-315. ACM, 2003. URL: https://doi.org/10.1145/780542.780589.
  11. Gerth Stølting Brodal, Rolf Fagerberg, Ulrich Meyer, and Norbert Zeh. Cache-oblivious data structures and algorithms for undirected breadth-first search and shortest paths. In Torben Hagerup and Jyrki Katajainen, editors, Algorithm Theory - SWAT 2004, 9th Scandinavian Workshop on Algorithm Theory, Humlebaek, Denmark, July 8-10, 2004, Proceedings, volume 3111 of Lecture Notes in Computer Science, pages 480-492. Springer, 2004. URL: https://doi.org/10.1007/978-3-540-27810-8_41.
  12. Gerth Stølting Brodal and Jyrki Katajainen. Worst-case external-memory priority queues. In Stefan Arnborg and Lars Ivansson, editors, Algorithm Theory - SWAT '98, 6th Scandinavian Workshop on Algorithm Theory, Stockholm, Sweden, July, 8-10, 1998, Proceedings, volume 1432 of Lecture Notes in Computer Science, pages 107-118. Springer, 1998. URL: https://doi.org/10.1007/BFB0054359.
  13. Mark R. Brown. Implementation and analysis of binomial queue algorithms. SIAM Journal of Computing, 7(3):298-319, 1978. URL: https://doi.org/10.1137/0207026.
  14. Svante Carlsson, J. Ian Munro, and Patricio V. Poblete. An implicit binomial queue with constant insertion time. In Rolf G. Karlsson and Andrzej Lingas, editors, SWAT 88, 1st Scandinavian Workshop on Algorithm Theory, Halmstad, Sweden, July 5-8, 1988, Proceedings, volume 318 of Lecture Notes in Computer Science, pages 1-13. Springer, 1988. URL: https://doi.org/10.1007/3-540-19487-8_1.
  15. Rezaul Alam Chowdhury and Vijaya Ramachandran. Cache-oblivious shortest paths in graphs using buffer heap. In Phillip B. Gibbons and Micah Adler, editors, SPAA 2004: Proceedings of the Sixteenth Annual ACM Symposium on Parallelism in Algorithms and Architectures, June 27-30, 2004, Barcelona, Spain, pages 245-254. ACM, 2004. URL: https://doi.org/10.1145/1007912.1007949.
  16. James R. Driscoll, Harold N. Gabow, Ruth Shrairman, and Robert Endre Tarjan. Relaxed heaps: An alternative to fibonacci heaps with applications to parallel computation. Communications of the ACM, 31(11):1343-1354, 1988. URL: https://doi.org/10.1145/50087.50096.
  17. Kasper Eenberg, Kasper Green Larsen, and Huacheng Yu. Decreasekeys are expensive for external memory priority queues. In Hamed Hatami, Pierre McKenzie, and Valerie King, editors, Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2017, Montreal, QC, Canada, June 19-23, 2017, pages 1081-1093. ACM, 2017. URL: https://doi.org/10.1145/3055399.3055437.
  18. R. Fadel, K. V. Jakobsen, Jyrki Katajainen, and Jukka Teuhola. Heaps and heapsort on secondary storage. Theoretical Computer Science, 220(2):345-362, 1999. URL: https://doi.org/10.1016/S0304-3975(99)00006-7.
  19. Michael L. Fredman and Robert Endre Tarjan. Fibonacci heaps and their uses in improved network optimization algorithms. Journal of the ACM, 34(3):596-615, 1987. URL: https://doi.org/10.1145/28869.28874.
  20. Matteo Frigo, Charles E. Leiserson, Harald Prokop, and Sridhar Ramachandran. Cache-oblivious algorithms. In 40th Annual Symposium on Foundations of Computer Science, FOCS '99, 17-18 October, 1999, New York, NY, USA, pages 285-298. IEEE Computer Society, 1999. URL: https://doi.org/10.1109/SFFCS.1999.814600.
  21. Matteo Frigo, Charles E. Leiserson, Harald Prokop, and Sridhar Ramachandran. Cache-oblivious algorithms. ACM Transactions on Algorithms, 8(1):4:1-4:22, 2012. URL: https://doi.org/10.1145/2071379.2071383.
  22. Bernhard Haeupler, Richard Hladík, Václav Rozhon, Robert E. Tarjan, and Jakub Tetek. Universal optimality of Dijkstra via beyond-worst-case heaps. In 65th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2024, Chicago, IL, USA, October 27-30, 2024, pages 2099-2130. IEEE, 2024. URL: https://doi.org/10.1109/FOCS61266.2024.00125.
  23. Bernhard Haeupler, Richard Hladík, Václav Rozhon, Robert E. Tarjan, and Jakub Tetek. Bidirectional Dijkstra’s algorithm is instance-optimal. In Ioana Oriana Bercea and Rasmus Pagh, editors, 2025 Symposium on Simplicity in Algorithms, SOSA 2025, New Orleans, LA, USA, January 13-15, 2025, pages 202-215. SIAM, 2025. URL: https://doi.org/10.1137/1.9781611978315.16.
  24. Nicholas J. A. Harvey and Kevin C. Zatloukal. The post-order heap. In Proceedings Third International Conference on Fun with Algorithms (FUN 2004), Elba, Italy, May 2004, 2004. URL: http://people.csail.mit.edu/nickh/Publications/PostOrderHeap/FUN04-PostOrderHeap.pdf.
  25. John Iacono, Riko Jacob, and Konstantinos Tsakalidis. External memory priority queues with decrease-key and applications to graph algorithms. In Michael A. Bender, Ola Svensson, and Grzegorz Herman, editors, 27th Annual European Symposium on Algorithms, ESA 2019, September 9-11, 2019, Munich/Garching, Germany, volume 144 of LIPIcs, pages 60:1-60:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. URL: https://doi.org/10.4230/LIPICS.ESA.2019.60.
  26. Shunhua Jiang and Kasper Green Larsen. A faster external memory priority queue with decreasekeys. In Timothy M. Chan, editor, Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019, San Diego, California, USA, January 6-9, 2019, pages 1331-1343. SIAM, 2019. URL: https://doi.org/10.1137/1.9781611975482.81.
  27. Vijay Kumar and Eric J. Schwabe. Improved algorithms and data structures for solving graph problems in external memory. In Proceedings of the Eighth IEEE Symposium on Parallel and Distributed Processing, SPDP 1996, New Orleans, Louisiana, USA, October 23-26, 1996, pages 169-176. IEEE Computer Society, 1996. URL: https://doi.org/10.1109/SPDP.1996.570330.
  28. Mark H. Overmars. The Design of Dynamic Data Structures, volume 156 of Lecture Notes in Computer Science. Springer, 1983. URL: https://doi.org/10.1007/BFB0014927.
  29. Nir Shavit and Itay Lotan. Skiplist-based concurrent priority queues. In Proceedings 14th International Parallel and Distributed Processing Symposium. IPDPS 2000, pages 263-268. IEEE, 2000. URL: https://doi.org/10.1109/IPDPS.2000.845994.
  30. Mikkel Thorup. On RAM priority queues. SIAM Journal on Computing, 30(1):86-109, 2000. URL: https://doi.org/10.1137/S0097539795288246.
  31. Jean Vuillemin. A data structure for manipulating priority queues. Communications of the ACM, 21(4):309-315, 1978. URL: https://doi.org/10.1145/359460.359478.
  32. John William Joseph Williams. Algorithm 232: Heapsort. Communications of the ACM, 7(6):347-348, 1964. URL: https://doi.org/10.1145/512274.512284.
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