A bridging model for parallel computation
Communications of the ACM
Efficient parallel algorithms for string editing and related problems
SIAM Journal on Computing
Parallel sorting by regular sampling
Journal of Parallel and Distributed Computing
General purpose parallel computing
Lectures on parallel computation
The bulk-synchronous parallel random access machine
Theoretical Computer Science - Special issue on parallel computing
The String-to-String Correction Problem
Journal of the ACM (JACM)
A fast algorithm for computing longest common subsequences
Communications of the ACM
Enumerating longest increasing subsequences and patience sorting
Information Processing Letters
Parallel Scientific Computation: A Structured Approach Using BSP and MPI
Parallel Scientific Computation: A Structured Approach Using BSP and MPI
Semi-local longest common subsequences in subquadratic time
Journal of Discrete Algorithms
Longest common subsequences in permutations and maximum cliques in circle graphs
CPM'06 Proceedings of the 17th Annual conference on Combinatorial Pattern Matching
A CGM algorithm solving the longest increasing subsequence problem
ICCSA'06 Proceedings of the 2006 international conference on Computational Science and Its Applications - Volume Part V
New algorithms for efficient parallel string comparison
Proceedings of the twenty-second annual ACM symposium on Parallelism in algorithms and architectures
A divide and conquer approach and a work-optimal parallel algorithm for the LIS problem
Information Processing Letters
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The longest increasing subsequence (LIS) problem is a classical problem in theoretical computer science and mathematics. Most existing parallel algorithms for this problem have very restrictive slackness conditions which prevent scalability to large numbers of processors. Other algorithms are scalable, but not work-optimal w.r.t. the fastest sequential algorithm for the LIS problem, which runs in time O(n log n) for n numbers in the comparison-based model. In this paper, we propose a new parallel algorithm for the LIS problem. Our algorithm solves the more general problem of semi-local comparison of permutation strings of length n in time O(n/1.5p) on p processors, has scalable communication cost of O(n/√p) and is synchronisation-efficient. Furthermore, we achieve scalable memory cost, requiring O(n/√p) of storage on each processor. When applied to LIS computation, this algorithm is superior to previous approaches since computation, communication, and memory costs are all scalable.