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Designing an oracle for a function

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Design an oracle for this function:
void compute_maximum_clique( �);
Input: a graph G(V,E), that is, V is a set of nodes and E is a set of edges connecting nodes in G.
Output: a sub-graph G'(V',E') of G such that for any two nodes u,v in V', there is an edge e=(u,v) in E'. In addition, G' should be the maximum in terms of the size. That is, for any other G'' with the above property, we have |G''| no larger than |G'|.

Hints: The clique problem itself is NP-hard. Thus you may not want to have an oracle that runs in exponential time. Think about approach to approximate the solution. In another word, design an oracle that runs efficiently but may make mistakes in some cases.

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Solution Summary

This solution designs an oracle for the following function:
void compute_maximum_clique( �);
Input: a graph G(V,E), that is, V is a set of nodes and E is a set of edges connecting nodes in G.
Output: a sub-graph G'(V',E') of G such that for any two nodes u,v in V', there is an edge e=(u,v) in E'. In addition, G' should be the maximum in terms of the size. That is, for any other G'' with the above property, we have |G''| no larger than |G'|.

Hints: The clique problem itself is NP-hard. Thus you may not want to have an oracle that runs in exponential time. Think about approach to approximate the solution. In another word, design an oracle that runs efficiently but may make mistakes in some cases

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This is the problem:

Tom Ashton started Ashton Manufacturing Inc (AMI) several years ago. The Company has grown quickly from a small operation to the mid-sized organization it is today. AMI has an opportunity to take on an additional customer. This arrangement will allow AMI to grow to a large organization operating nearly 24 hours a day / 7 days a week.

Recently AMI has been experiencing significant downtime due to a failing software application written for AMI when the company started. This Access database application is responsible for a key manufacturing process.

Mr. Ashton and his investors are concerned the Company can not grow until the technical infrastructure is in place and functioning properly. AMI has limited funds for IT endeavors but has hired your consulting firm seeking advice.

Objective:

Prepare a 1-page executive summary including your recommendations to repair or replace the application. Support this summary with a research paper which contains the details behind the summary.

Start by researching Microsoft Access and other prominent RDBMS such as MS SQL Server, Oracle and My SQL. Compare and contrast these systems based on key features such as scalability, ease of implementation (development and support), performance, security and price.

Include a discussion on SQL:

What is SQL?
Who owns SQL?
What are some of the differences in the SQL supported by RDBMS vendors?

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