Search versus decision. Suppose you have a procedure which...

Name: Problem 2, Chapter 8: Algorithms
Uploaded: 2019-10-25T17:54:31-08:00
Duration: 36 s
Channel: Wen Zheng
Description: Search versus decision. Suppose you have a procedure which runs in polynomial time and tells you whether or not a graph has a Rudrata path. Show that you can use it to develop a polynomialtime algorithm for RUDRATA PATH (which returns the actual path, if it exists).

Search versus decision. Suppose you have a procedure which runs in polynomial time and tells you whether or not a graph has a Rudrata path. Show that you can use it to develop a polynomialtime algorithm for RUDRATA PATH (which returns the actual path, if it exists).

Key Concepts

Decision Problem

A decision problem asks for a yes/no answer about whether a solution exists for a given instance. In algorithm theory, decision procedures determine the existence of a certain structure or property without necessarily constructing the solution. This forms the basis for determining membership in complexity classes like NP.

Search Problem

A search problem not only asks whether a solution exists but requires the actual solution (e.g., an object or sequence) to be output if one exists. This is more challenging than a decision problem since it involves constructing the specific structure that satisfies a given property.

Self-Reducibility

Self-reducibility is a method where a solution to a search problem is obtained by making a sequence of calls to a decision algorithm. By systematically modifying the problem instance and asking the decision question at each step, one can piece together a complete solution. This technique shows that under certain conditions, a decision procedure can be harnessed to solve the search problem in polynomial time.

Polynomial-Time Reduction

Polynomial-time reduction is the strategy of transforming one computational problem into another in a way that the transformation itself takes only polynomial time. This concept is crucial when using a polynomial-time decision algorithm to solve a search problem, as it ensures that the overall process of constructing the solution remains efficient.

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