Some triply-logarithmic parallel algorithms

It is established that several natural problems have triply logarithmic, or even faster, optimal parallel algorithms. These problems include: merging two sorted lists, where the values are drawn from a large, but restricted, domain on a CREW PRAM; finding all prefix minima, where the values are drawn from a restricted domain; and top-bottom global routing around a rectangle, a well-investigated problem in VLSI routing for which only highly involved serial algorithms were known.<<ETX>>

[1]  Ilan Adler,et al.  A Strongly Polynomial Algorithm for a Special Class of Linear Programs , 1991, Oper. Res..

[2]  D. Eppstein,et al.  Parallel Algorithmic Techniques for Combinatorial Computation , 1988 .

[3]  Uzi Vishkin,et al.  Highly parallelizable problems , 1989, STOC '89.

[4]  Uzi Vishkin,et al.  Deterministic sampling—a new technique for fast pattern matching , 1990, STOC '90.

[5]  Nimrod Megiddo,et al.  Linear programming with two variables per inequality in poly-log time , 1986, STOC '86.

[6]  Andrew V. Goldberg,et al.  Combinatorial Algorithms for the Generalized Circulation Problem , 1991, Math. Oper. Res..

[7]  Edith Cohen,et al.  New Algorithms for Generalized Network Flows , 1992, ISTCS.

[8]  Allen Van Gelder.  PRAM Processor Allocation: A Hidden Bottleneck in Sublogarithmic Algorithms , 1989, IEEE Trans. Computers.

[9]  Johan Håstad,et al.  Optimal bounds for decision problems on the CRCW PRAM , 1987, STOC.

[10]  Sanguthevar Rajasekaran,et al.  Optimal and Sublogarithmic Time Randomized Parallel Sorting Algorithms , 1989, SIAM J. Comput..

[11]  Nimrod Megiddo,et al.  Applying parallel computation algorithms in the design of serial algorithms , 1981, 22nd Annual Symposium on Foundations of Computer Science (sfcs 1981).

[12]  Larry Rudolph,et al.  Counting and Packing in Parallel , 1986, ICPP.

[13]  Abraham Charnes,et al.  One-Pass Algorithms for Some Generalized Network Problems , 1966, Oper. Res..

[14]  Uzi Vishkin,et al.  Finding all nearest neighbors for convex polygons in parallel: A new lower bound technique and a matching algorithm , 1990, Discret. Appl. Math..

[15]  Uzi Vishkin,et al.  Finding the maximum, merging and sorting in a parallel computation model , 1981, CONPAR.

[16]  Brenda S. Baker.  A Provably Good Algorithm for the Two Module Routing Problem , 1986, SIAM J. Comput..

[17]  Friedhelm Meyer auf der Heide,et al.  The complexity of parallel sorting , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[18]  L. G. H. Cijan.  A polynomial algorithm in linear programming , 1979 .

[19]  Nimrod Megiddo,et al.  Combinatorial optimization with rational objective functions , 1978, Math. Oper. Res..

[20]  Andrea S. LaPaugh,et al.  A polynomial time algorithm for optimal routing around a rectangle , 1980, 21st Annual Symposium on Foundations of Computer Science (sfcs 1980).

[21]  Leslie G. Valiant,et al.  Parallelism in Comparison Problems , 1975, SIAM J. Comput..

[22]  Clyde P. Kruskal,et al.  Searching, Merging, and Sorting in Parallel Computation , 1983, IEEE Transactions on Computers.

[23]  Stephen A. Cook,et al.  Upper and Lower Time Bounds for Parallel Random Access Machines without Simultaneous Writes , 1986, SIAM J. Comput..

[24]  Yijie Han,et al.  Matching partition a linked list and its optimization , 1989, SPAA '89.

[25]  Edith Cohen,et al.  Improved algorithms for linear inequalities with two variables per inequality , 1991, STOC '91.

[26]  Nesa L'abbe Wu,et al.  Linear programming and extensions , 1981 .

[27]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

[28]  Teofilo F. Gonzalez,et al.  A linear time algorithm for optimal routing around a rectangle , 1988, JACM.

[29]  Nimrod Megiddo,et al.  Towards a Genuinely Polynomial Algorithm for Linear Programming , 1983, SIAM J. Comput..

[30]  David Eppstein,et al.  Parallel Algorithmic Techniques for Combinatorial Computation , 1988, ICALP.

[31]  Majid Sarrafzadeh,et al.  A bottom-up layout technique based on two-rectangle routing , 1987, Integr..

[32]  Richard Cole,et al.  Deterministic Coin Tossing with Applications to Optimal Parallel List Ranking , 2018, Inf. Control..

[33]  Stephen Warshall,et al.  A Theorem on Boolean Matrices , 1962, JACM.

[34]  Torben Hagerup,et al.  Towards Optimal Parallel Bucket Sorting , 1987, Inf. Comput..

[35]  Allan Borodin,et al.  Routing, merging and sorting on parallel models of computation , 1982, STOC '82.

[36]  Uzi Vishkin,et al.  On Parallel Hashing and Integer Sorting (Extended Summary) , 1990, ICALP.

[37]  Andrew V. Goldberg,et al.  Combinatorial algorithms for the generalized circulation problem , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[38]  Allan Borodin,et al.  Routing, Merging, and Sorting on Parallel Models of Computation , 1985, J. Comput. Syst. Sci..