cse101-w12-intro-final

cse101-w12-intro-final - CSE 101, Winter 2012 Design and...

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CSE 101, Winter 2012 Design and Analysis of Algorithms Instructor: Prof. Andrew B. Kahng Webpage: http://vlsicad.ucsd.edu/~abk/ Email: abk@cs.ucsd.edu Telephone: 858-822-4884 Office Hours: Wed 12:30-1:30pm, Fri noon-1pm, by appt Office: EBU3B 2134 Class URL: http://vlsicad.ucsd.edu/courses/cse101-w12/
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Goals of Course • Introduction to design and analysis of algorithms • “Problem-solving” • Classic Problems – Sorting, Path-Finding, String-Matching, Arithmetic, … • Tools – Recurrence Relations, Counting Techniques, Reduction, Probabilistic Analysis, NP-Completeness, … • Frameworks – Divide-and-Conquer, Greed, Dynamic Programming, Branch-and- Bound, Heuristics, … • Pedagogical choices – Order of material – “Analyze” vs. “Create” I stress the latter = problem-solving – Scope You need to keep up
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What Is An Algorithm ? • An algorithm is a method for solving a problem (on a computer) Problem: “Given fraction m/n, reduce to lowest terms.” • An algorithm must be effective give a correct answer and terminate Problem: Given undirected graph G = (V,E) and vertices s,t V, is there a path in G from s to t ?” QUESTION: State an algorithm for this problem
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Undirected s-t Connectivity • A1: BFS, DFS from s. • A2: Take a random walk in G, starting at s. Is this an algorithm? (Does it halt?) • A3: Take a random walk in G for 5n 3 steps starting at s (n = |V|); return NO iff we don’t visit t. Is this an algorithm? Does it “almost always” return the correct answer? • Do A3, A1 differ in terms of resources used? – A3 “trades” time for space, is “memoryless”. – A3: probabilistic effectiveness. G = (V,E) s t t’
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Problem-Solving • Problem solving = “The Spirit of Computing” • Driven by real-world necessity – DNA Sequencing • Evolutionary Trees (edit distance, Steiner trees. ..) • Finding homologues, evolutionary significance (string-match) – Conformational Analysis • Drug Design (min-energy state) – Autonomous Robotics, Vehicles • (managing smart highways, collision avoidance / path planning, …) – Logistics • (scheduling, resource allocation, …) – Design of integrated circuits • (placement, wiring, partitioning, floorplanning, clock distribution, logic synthesis, …)
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Problem-Solving • Patterns – Zeitz, The Art and Craft of Problem Solving – Polya, How to Solve It • Tools – Counting – Recurrence Relations – Data Structures –… • Concepts – Problem classes and “solution classes” – Lower bounds at least this hard, at least this effort … – Reductions solving this boils down to solving that … – Intractability believed impossible to solve efficiently …
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What is a Problem? • A problem is defined by:
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cse101-w12-intro-final - CSE 101, Winter 2012 Design and...

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