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Randomized parallel algorithms for trapezoidal diagrams
Abstract: "We describe randomized parallel CREW PRAM algorithms for building trapezoidal diagrams of line segments in the plane. For general segments, we give an algorithm requiring optimal O(A + n log n) expected work and optimal O(log n) time, where A is the number of intersecting pairs of segments. If the segments form a simple chain, we give an algorithm requiring optimal O(n) expected work and O(log n log log n log* n) expected time, and a simpler algorithm requiring O(n log* n) expected work. The serial algorithm corresponding to the latter is the simplest known algorithm requiring O(n log* n) expected operations.
- "Abstract: "We describe randomized parallel CREW PRAM algorithms for building trapezoidal diagrams of line segments in the plane. For general segments, we give an algorithm requiring optimal O(A + n log n) expected work and optimal O(log n) time, where A is the number of intersecting pairs of segments. If the segments form a simple chain, we give an algorithm requiring optimal O(n) expected work and O(log n log log n log* n) expected time, and a simpler algorithm requiring O(n log* n) expected work. The serial algorithm corresponding to the latter is the simplest known algorithm requiring O(n log* n) expected operations."@en
- "For a set of segments forming K chains, we give an algorithm requiring O(A + n log* n + K log n) expected work and O(log n log log n log* n) expected time. The parallel time bounds require the assumption that enough processors are available, with processor allocations every log n steps.""@en
- "Randomized parallel algorithms for trapezoidal diagrams"
- "Randomized parallel algorithms for trapezoidal diagrams"@en