A Partitioning Strategy for Nonuniform Problems on Multiprocessors
IEEE Transactions on Computers
Integer and combinatorial optimization
Integer and combinatorial optimization
Solving problems on concurrent processors. Vol. 1: General techniques and regular problems
Solving problems on concurrent processors. Vol. 1: General techniques and regular problems
Partitioning Problems in Parallel, Pipeline, and Distributed Computing
IEEE Transactions on Computers
Approximation algorithms for hitting objects with straight lines
Discrete Applied Mathematics
Improved Algorithms for Mapping Pipelined and Parallel Computations
IEEE Transactions on Computers
Rectilinear partitioning of irregular data parallel computations
Journal of Parallel and Distributed Computing
On the Complexity of the Generalized Block Distribution
IRREGULAR '96 Proceedings of the Third International Workshop on Parallel Algorithms for Irregularly Structured Problems
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
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We provide constant ratio approximation algorithms for two NP-hard problems, the rectangle stabbing problem and the rectilinear partitioning problem. In the rectangle stabbing problem, we are given a set of rectangles in two-dimensional space, with the objective of stabbing all rectangles with the minimum number of lines parallel to the x and y axes. We provide a 2-approximation algorithm, while the best known approximation ratio for this problem is O(log n). This algorithm is then extended to a 4-approximation algorithm for the rectilinear partitioning problem, which, given an m × n array of non-negative integers, asks to find a set of vertical and horizontal lines such that the maximum load of a subrectangle (i.e., the sum of the numbers in it) is minimized. This problem arises when a mapping of an m × n array onto an h × v mesh of processors is required such that the largest load assigned to a processor is minimized. The best known approximation ratio for this problem is 27. Our approximation ratio 4 is close to the best possible, as there is evidence that it is NP-hard to approximate within a factor of 2.