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# lec17 - Click to edit Master subtitle style Sundar B CS...

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Unformatted text preview: Click to edit Master subtitle style 2/7/11 Sundar B. CS C341 / I S C361 Data Structures & Algorithms Partially Ordered Data Totally Ordered Data vs. Partially Ordered Data- ADT Priority Queue Data Structure for Priority Queue- A Heap- Representation (Binary Trees and Arrays)- Implementation of Operations Other Applications of Heaps- Heap Sort: Algorithm, Complexity, Comparisons 11 2/7/11 Sundar B. 2/7/11 Sundar B. Partial Order A (binary) relation R, subset of S x S,&is said to be a partial order if (it is reflexive: x R x for all x in S) it is transitive: x R y and y R z implies x R z for x,y,z in S it is anti-symmetric: x R y and y R x implies x = y Example “is an ancestor of” on persons “under-writes” on companies Question: 2/7/11 22 Sundar B. 2/7/11 Sundar B. Total Order A (binary) relation R, subset of S x S, is said to be a total order if x R y OR y R x for any x and y in S. Examples: <= on real numbers “is at least as old as” on persons 2/7/11 33 Sundar B. 2/7/11 Sundar B. Total Order vs. Partial Order Implications: 5th element? Minimum element? Linear Order – Refer Discrete Structures Least common ancestor Join and Meet – Refer Discrete Structures E.g. Tournament Trees: For a Tennis tournament (or any knock-out pairing based tournament) Given pairing information predict who may meet whom at a later stage 2/7/11 44 Sundar B. 2/7/11 Sundar B. Total Order vs. Partial Order Application: Consider a multi-processing operating system More than one process could be waiting (for CPU) Processes are to be scheduled No self knowledge or co-ordination among processes Need a queue for “ ready” processes Need a strategy for adding/deleting processes 2/7/11 55 Sundar B. 2/7/11...
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lec17 - Click to edit Master subtitle style Sundar B CS...

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