# lec6 - CS575 Parallel Processing Lecture six Searching Wim...

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CS575 lecture 6 2 Search and Discrete Optimization Discrete Optimization Problem (S,f) S: space of feasible solutions (satisfying some constraints) f : S R function that maps all feasible solutions on the real numbers Objective: find an optimal solution x opt such that f(x opt )<= f(x) for all x in S or f(x opt )>= f(x) for all x in S Search application domains planning and scheduling VLSI layout pattern recognition
CS575 lecture 6 3 Example: 0/1 integer linear programming Given m x n constraint matrix A m x 1 vector b 1 x m vector c Objective: Find a 0/1 vector x s.t. A . x b c. x minimal

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CS575 lecture 6 4 Example: 8 puzzle Given: 3x3 grid with 8 tiles (number 1 to 8) one hole Tiles can slide into the hole if they are adjacent Objective: Given an initial configuration, determine a minimal sequence of moves to create (say) 1 2 3 4 5 6 7 8
CS575 lecture 6 5 State Space Graph corresponding to space of feasible solutions Nodes are called states Terminal nodes have no successors Optimization problem reformulated as finding a minimal cost path through the graph from initial node to a goal node Examples reformulated as graphs 0/1 integer linear programming (Example 11.1) 8 puzzle (Example 11.2)

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CS575 lecture 6 6 Example: Knapsack problem Is a 0/1 ILP problem Given n objects - each with weight w i and profit p i a knapsack with capacity M Determine a subset of the objects such that total weight M total profit maximal
CS575 lecture 6 7 State space for knapsack State space is a tree Information stored per state 1. Capacity left. 2. Profit gathered. 3. Objects taken Root level 0: no object has been considered

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## This note was uploaded on 09/24/2009 for the course CS 525 taught by Professor Rjyosy during the Winter '09 term at Central Mich..

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lec6 - CS575 Parallel Processing Lecture six Searching Wim...

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