In tight compaction one is given an array of balls some of which are marked 0 and the rest are marked 1. The output of the procedure is an array that contains all of the original balls except that now the 0-balls appear before the 1-balls. In other words, tight compaction is equivalent to sorting the array according to 1-bit keys (not necessarily maintaining order within same-key balls). Tight compaction is not only an important algorithmic task by itself, but its oblivious version has also played a key role in recent constructions of oblivious RAM compilers. We present an oblivious deterministic algorithm for tight compaction such that for input arrays of n balls requires O(n) total work and O(log n) depth. Our algorithm is in the Exclusive-Read-Exclusive-Write Parallel-RAM model (i.e., EREW PRAM, the most restrictive PRAM model), and importantly we achieve asymptotical optimality in both total work and depth. To the best of our knowledge no earlier work, even when allowing randomization, can achieve optimality in both total work and depth.
|Title of host publication||1st Conference on Information-Theoretic Cryptography, ITC 2020|
|Editors||Yael Tauman Kalai, Adam D. Smith, Daniel Wichs|
|Publisher||Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing|
|State||Published - 1 Jun 2020|
|Event||1st Conference on Information-Theoretic Cryptography, ITC 2020 - Virtual, Boston, United States|
Duration: 17 Jun 2020 → 19 Jun 2020
|Name||Leibniz International Proceedings in Informatics, LIPIcs|
|Conference||1st Conference on Information-Theoretic Cryptography, ITC 2020|
|Period||17/06/20 → 19/06/20|
Bibliographical noteFunding Information:
Funding Wei-Kai Lin: Wei-Kai Lin supported by NSF CNS-1453634, an ONR YIP award, a Packard Fellowship, and a DARPA Brandeis grant. Elaine Shi: Elaine Shi supported by NSF CNS-1453634, an ONR YIP award, a Packard Fellowship, and a DARPA Brandeis grant.
© Gilad Asharov, Ilan Komargodski, Wei-Kai Lin, Enoch Peserico, and Elaine Shi; licensed under Creative Commons License CC-BY
- EREW PRAM
- Oblivious tight compaction
- Parallel oblivious RAM