Top-bottom routing around a rectangle is as easy as computing prefix minima
O Berkman, J Jaja, S Krishnamurthy, R Thurimella… - SIAM journal on …, 1994 - SIAM
SIAM journal on computing, 1994•SIAM
A new parallel algorithm for the prefix minima problem is presented for inputs drawn from the
range of integers 1..s. For an input of size n, it runs in O(\log\log\logs) time and O(n) work
(which is optimal). A faster algorithm is presented for the special case s=n; it runs in
O(\log^*n) time with optimal work. Both algorithms are for the Priority concurrent-read
concurrent-write parallel random access machine (CROW PRAM). A possibly surprising
outcome of this work is that, whenever the range of the input is restricted, the prefix minima …
range of integers 1..s. For an input of size n, it runs in O(\log\log\logs) time and O(n) work
(which is optimal). A faster algorithm is presented for the special case s=n; it runs in
O(\log^*n) time with optimal work. Both algorithms are for the Priority concurrent-read
concurrent-write parallel random access machine (CROW PRAM). A possibly surprising
outcome of this work is that, whenever the range of the input is restricted, the prefix minima …
A new parallel algorithm for the prefix minima problem is presented for inputs drawn from the range of integers . For an input of size n, it runs in time and work (which is optimal). A faster algorithm is presented for the special case ; it runs in time with optimal work. Both algorithms are for the Priority concurrent-read concurrent-write parallel random access machine (CROW PRAM). A possibly surprising outcome of this work is that, whenever the range of the input is restricted, the prefix minima problem can be solved significantly faster than the time lower bound in a decision model of parallel computation, as described by Valiant [SIAM J. Comput., 4 (1975), pp. 348–355].
The top-bottom routing problem, which is an important subproblem of routing wires around a rectangle in two layers, is also considered. It is established that, for parallel (and hence for serial) computation, the problem of top-bottom routing is no harder than the prefix minima problem with , thus giving an time optimal parallel algorithm for the top-bottom routing problem. This is one of the first nontrivial problems to be given an optimal parallel algorithm that runs in sublogarithmic time.

Showing the best result for this search. See all results