ALGTYPE

# ALGTYPE - ALGORITHM TYPES • Greedy Divide and Conquer...

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Unformatted text preview: ALGORITHM TYPES • Greedy, Divide and Conquer, Dynamic Programming, Random Algorithms, and Backtracking. • Note the general strategy from the examples. • The classification is neither exhaustive (there may be more) nor mutually exclusive (one may combine). • We are now emphasizing design of algorithms, not data structures. GREEDY: Some Scheduling problems • Scheduling Algorithm: Optimizing function is aggregate finish-time with one processor • (job-id, duration pairs)::(j1, 15), (j2, 8), (j3, 3), (j4, 10): aggregate FT in this order is 15+23+26+36=100 • Note: durations of tasks are getting added multiple times: 15 + (15+8) + ((15+8) + 3) + . . . • Optimal schedule is the Greedy schedule: j3, j2, j4, j1. Aggregate FT=3+11+21+36=71 [Let the lower values get added more times: shortest job first ] • Sort: O (n log n) , + Placing: Θ (n), • Total: O(n log n) , MULTI-PROCESSOR SCHEDULING (Aggregate FT) • Optimizing Fn. Aggregate FT - Strategy: Assign pre-ordered jobs over processors one by one • Input (job-id, duration)::(j2, 5), (j1, 3), (j5, 11), (j3, 6), (j4, 10), (j8, 18), (j6, 14), (j7, 15), (j9, 20): 3 proc • Sort first: (j1, 3), (j2, 5), (j3, 6), (j4, 10), (j5, 11), (j6, 14), (j7, 15), (j8, 18), (j9, 20) // O (n log n) • Schedule next job on earliest available processor • Proc 1: j1, j4, j7 Proc 2: j2, j5, j8 Proc 3: j3, j6, j9 // Sort: Theta(n log n), Place: Theta(n), Total: Theta(n log n) • Note the first task is to order jobs for a “greedy” pick up • Optimizing Fn. Last FT - Strategy: Sort jobs in reverse order, assign next job on the earliest available processor • (j3, 6), (j1, 3), (j2, 5), (j4, 10), (j6, 14), (j5, 11), (j8, 18), (j7, 15), (j9, 20): 3 proc • Reverse sort- • (j9, 20), (j8, 18), (j7, 15), (j6, 14), (j5, 11), (j4, 10), (j3, 6), (j2, 5), (j1, 3) • Proc 1: j9 - 20, j4 - 30, j1 - 33. • Proc 2: j8 - 18, j5 - 29, j3 - 35, • Proc 3: j7 - 15, j6 - 29, j2 - 34, Last FT = 35. • // sort: O(n log n) • // place: naïve: Θ (nM), with heap over processors: O (n log m) • Optimal: Proc1: j2, j5, j8; Proc 2: j6, j9; Proc 3: j1, j3, j4, j7. Last FT = 34. • Greedy alg is not optimal algorithm here, but the relative err <= [1/3 - 1/3m], for m processors. • An NP-complete problem, greedy alg is polynomial O(n logn) for n jobs (from sorting, assignment is additional O(n), choice of next proc. In each cycle O(log m) using heap, total O(n logn + n logm), for n>>m the first term dominates). MULTI-PROCESSOR SCHEDULING (Last FT) HUFFMAN CODES • Problem: device a (binary) coding of alphabets for a text, given their frequency in the text, such that the total number of bits in the translation is minimum....
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ALGTYPE - ALGORITHM TYPES • Greedy Divide and Conquer...

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