'3 sat' diaporamas de présentation

NP-Completeness

NP-Completeness. Decision Problems. Given Some Universal Set X, Let R be a subset of X. The decision problem for R is: Given an arbitrary element a of X, does a belong to R? Note: X is usually assumed to be a set of strings, but this can be interpreted loosely. The class P.

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Constrainedness of Search

Constrainedness of Search. Toby Walsh NICTA and UNSW http://cse.unsw.edu.au/~tw. Motivation. Will a problem be satisfiable or unsatisfiable? Will it be hard or easy? How can we develop heuristics for a new problem?. Take home messages.

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Molecular Computing: Challenges across the two tracks in Theoretical Computer Science

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The TSP : NP-Completeness Approximation and Hardness of Approximation

*. The TSP : NP-Completeness Approximation and Hardness of Approximation. All exact science is dominated by the idea of approximation. -- Bertrand Russell (1872 - 1970). Based upon slides of Dana Moshkovitz, Kevin Wayne and others + some old slides.

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Where are the hard problems?

Where are the hard problems?. Patrick Prosser with help from Peter Cheeseman Bob Kanefsky Will Taylor APES and many more. Where are the hard problems?. Remember Graph Colouring?. Remember 3Col?. 3 Colour me?. 3 Colour me?. Easy?. 3 Colour me?. 3 Colour me?. Easy?. 3 Colour me?.

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NP-Completeness

NP-Completeness. Observation. All problems below are NP-complete and polynomial reduce to one another!. by definition of NP-completeness. CIRCUIT-SAT. 3-SAT. 3-SAT reduces to INDEPENDENT SET. INDEPENDENT SET. DIR-HAM-CYCLE. GRAPH 3-COLOR. SUBSET-SUM. VERTEX COVER. SCHEDULING.

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The Rectilinear Steiner Arborescence Problem is NP-Complete

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Black-box (oracle)

Black-box (oracle). Feed me a weighted graph G and I will tell you the weight of the max-weight matching of G. Black-box (oracle). 5. Feed me a weighted graph G and I will tell you the weight of the max-weight matching of G. 2. 2. Black-box (oracle). 5.

490 views • 41 slides

More NP-Complete Problems

More NP-Complete Problems. NP-Hard Problems Tautology Problem Node Cover Knapsack. Next Steps. We can now reduce 3-SAT to a large number of problems, either directly or indirectly. Each reduction must be polytime.

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Prof. Swarat Chaudhuri

COMP 482: Design and Analysis of Algorithms. Prof. Swarat Chaudhuri. Spring 2013 Lecture 22. Definition of P. P. Decision problems for which there is a poly-time algorithm. NP. Certification algorithm intuition. Certifier views things from "managerial" viewpoint.

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The P C P starting point

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NP Completeness

NP Completeness. Piyush Kumar. Today. Reductions Proving Lower Bounds revisited Decision and Optimization Problems SAT and 3-SAT P Vs NP Dealing with NP-Complete Problems Average Case / Heuristics / Approx. Alg. Convex Hulls and Sorting. What are convex hulls?

457 views • 28 slides

The Connectivity of Boolean Satisfiability: Structural and Computational Dichotomies

The Connectivity of Boolean Satisfiability: Structural and Computational Dichotomies. Elitza Maneva (UC Berkeley) Joint work with Parikshit Gopalan, Phokion Kolaitis and Christos Papadimitriou. Features of our dichotomy. Refers to the structure of the entire space of solutions

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DNA computing using single-molecule hybridization detection

DNA computing using single-molecule hybridization detection. K.A.Schmidt, C.V.Henkel, G.Rozenberg, and H.P.Spaink, NAR , vol. 32, no. 17, Sep. 2004, pp. 4962-4968. Summarized by Byoung-Hee Kim 2004.11.20. Overview. Problem: 3-SAT Algorithm: blocking algorithm Experiment Synthesis

291 views • 17 slides

CS 4700: Foundations of Artificial Intelligence

CS 4700: Foundations of Artificial Intelligence. Carla P. Gomes gomes@cs.cornell.edu Module: Instance Hardness and Phase Transitions (Reading R&N: page 224-225). Instance Hardness. Beyond NP-Completeness. NP-Completeness is a worst-case notion! Not all problems instances are the same!

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Lecture 22 More NPC problems

Lecture 22 More NPC problems. Today, we prove three problems to be NP-complete 3CNF-SAT Clique problem Vertex cover. Dick Karp. 3-CNF SAT is NP-complete.

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The Complexity of Linear Dependence Problems in Vector Spaces

The Complexity of Linear Dependence Problems in Vector Spaces. David Woodruff IBM Almaden Joint work with Arnab Bhattacharyya, Piotr Indyk, and Ning Xie from MIT. The 3-SUM Problem. Given a set S containing r real numbers, are there: a, b, c 2 S with a+b+c = 0? Solve in O(r 2 ) time

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Traveling Salesperson Problem

32. Traveling Salesperson Problem. TSP : Given a set of n cities and a pairwise distance function d(u, v), is there a tour of length ? D?. All 13,509 cities in US with a population of at least 500 Reference: http://www.tsp.gatech.edu. Traveling Salesperson Problem.

570 views • 16 slides

Reduction By Simple Equivalence

Reduction By Simple Equivalence. Basic reduction strategies. Reduction by simple equivalence. Reduction from special case to general case. Reduction by encoding with gadgets. Independent Set.

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( ???? ) 3-SAT ???? : V, ??? : C ? literal (x i , ? x i ) ??? 2 ???

75 views • 1 slides