Pointer jumping requires concurrent read

Noam Nisan; Ziv Bar-Yossef

doi:10.1145/258533.258648

Pointer jumping requires concurrent read

Noam Nisan^*, Ziv Bar-Yossef

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Contribution to journal › Conference article › peer-review

3 Scopus citations

Abstract

We consider the well known problem of determining the k'th vertex reached by chasing pointers in a directed graph of out-degree 1. The famous `pointer doubling' technique provides an O(log k) parallel time algorithm on a Concurrent-Read Exclusive-Write (CREW) PRAM. We prove that this problem requires Ω(k) steps on an Exclusive-Read Exclusive-Write (EREW) PRAM, for every k≤c√log n, where n is the number of vertices and c is a constant. This yields a boolean function which can be computed in O(log log n) time on a CREW PRAM, but requires Ω(√log n) time on even an `ideal' EREW PRAM. This is the first separation known for boolean functions between the power of EREW and CREW PRAMs. Previously, separations between EREW and CREW PRAMs were only known for functions on `huge' input domains, or for restricted types of EREW PRAMs.

Original language	American English
Pages (from-to)	549-558
Number of pages	10
Journal	Conference Proceedings of the Annual ACM Symposium on Theory of Computing
DOIs	https://doi.org/10.1145/258533.258648
State	Published - 1997
Event	Proceedings of the 1997 29th Annual ACM Symposium on Theory of Computing - El Paso, TX, USA Duration: 4 May 1997 → 6 May 1997

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title = "Pointer jumping requires concurrent read",

abstract = "We consider the well known problem of determining the k'th vertex reached by chasing pointers in a directed graph of out-degree 1. The famous `pointer doubling' technique provides an O(log k) parallel time algorithm on a Concurrent-Read Exclusive-Write (CREW) PRAM. We prove that this problem requires Ω(k) steps on an Exclusive-Read Exclusive-Write (EREW) PRAM, for every k≤c√log n, where n is the number of vertices and c is a constant. This yields a boolean function which can be computed in O(log log n) time on a CREW PRAM, but requires Ω(√log n) time on even an `ideal' EREW PRAM. This is the first separation known for boolean functions between the power of EREW and CREW PRAMs. Previously, separations between EREW and CREW PRAMs were only known for functions on `huge' input domains, or for restricted types of EREW PRAMs.",

author = "Noam Nisan and Ziv Bar-Yossef",

year = "1997",

doi = "10.1145/258533.258648",

language = "American English",

pages = "549--558",

journal = "Conference Proceedings of the Annual ACM Symposium on Theory of Computing",

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publisher = "Association for Computing Machinery (ACM)",

note = "Proceedings of the 1997 29th Annual ACM Symposium on Theory of Computing ; Conference date: 04-05-1997 Through 06-05-1997",

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AU - Nisan, Noam

AU - Bar-Yossef, Ziv

PY - 1997

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N2 - We consider the well known problem of determining the k'th vertex reached by chasing pointers in a directed graph of out-degree 1. The famous `pointer doubling' technique provides an O(log k) parallel time algorithm on a Concurrent-Read Exclusive-Write (CREW) PRAM. We prove that this problem requires Ω(k) steps on an Exclusive-Read Exclusive-Write (EREW) PRAM, for every k≤c√log n, where n is the number of vertices and c is a constant. This yields a boolean function which can be computed in O(log log n) time on a CREW PRAM, but requires Ω(√log n) time on even an `ideal' EREW PRAM. This is the first separation known for boolean functions between the power of EREW and CREW PRAMs. Previously, separations between EREW and CREW PRAMs were only known for functions on `huge' input domains, or for restricted types of EREW PRAMs.

AB - We consider the well known problem of determining the k'th vertex reached by chasing pointers in a directed graph of out-degree 1. The famous `pointer doubling' technique provides an O(log k) parallel time algorithm on a Concurrent-Read Exclusive-Write (CREW) PRAM. We prove that this problem requires Ω(k) steps on an Exclusive-Read Exclusive-Write (EREW) PRAM, for every k≤c√log n, where n is the number of vertices and c is a constant. This yields a boolean function which can be computed in O(log log n) time on a CREW PRAM, but requires Ω(√log n) time on even an `ideal' EREW PRAM. This is the first separation known for boolean functions between the power of EREW and CREW PRAMs. Previously, separations between EREW and CREW PRAMs were only known for functions on `huge' input domains, or for restricted types of EREW PRAMs.

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Pointer jumping requires concurrent read

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