Consider the bipartite matching problem introduced in Section 12–4. When a vertex bi of B arrives, we let bi match the nearest unmatched vertex of set R. Is such an algorithm (2n 1)-competitive? Prove your answer. Is the obstacle traversal algorithm introduced in Section 12–3 3/2-competitive for square obstacles with arbitrary directions? Prove your answer. ...

Nov 29 2021

Given a bipartite weighted graph with vertices bipartition R and B, each of cardinality n, the maximum bipartite matching problem is to find a bipartite matching with the maximum cost. Assume that all the weights of edges satisfy the triangle inequality. If the vertices in R are all known to us in advance and the vertices in B are revealed one by one, what is the competitive ratio of a greedy...

Nov 29 2021

Use the algorithm introduced in Section 11–5 to determine whether 5 is a quadratic residue of 13 or not. Show an example in which you would draw a wrong conclusion. Read Section 8–5 and 8–6 of Brassard and Bratley 1988. Prove that the on-line k-server algorithm introduced in Section 12–2 is also k-competitive for a line.

Nov 29 2021

Select any algorithm introduced in this chapter and implement it. Perform some experiments to see if the amortized analysis makes sense. Read Sleator and Tarjan (1983) on the dynamic tree data structure . Write a program to implement the randomized algorithm for solving the closest pair problem. Test your algorithms. Use the randomized prime number testing algorithm to determine whether the...

Nov 29 2021

Amortized analysis somehow implies that the concerned data structure has a certain self-organizing mechanism. In other words, when it becomes very bad, there is a chance that it will become good afterwards. In this sense, can hashing be analyzed by using amortized analysis? Do some research on this topic. You may be able to publish some papers, perhaps.

Nov 29 2021

Imagine that there is a person whose sole income is his monthly salary, which is k units per month. He can, however, spend any amount of money as long as his bank account has enough such money. He puts k units of income into his bank account every month. Can you perform an amortized analysis on his behavior? (Define your own problem. Note that he cannot withdraw a large amount of money all the...

Nov 29 2021

Read Section 12.3 of Horowitz and Sahni (1978) about approximation algorithms for scheduling independent tasks. Apply the longest processing time (LPT) rule to the following scheduling problem: There are three processors and seven tasks, where task times are (t1, t2, t3, t4, t5, t6, t7) (14, 12, 11, 9, 8, 7, 1). Write a program to implement the approximation algorithm for the traveling...

Nov 29 2021

Consider the following bottleneck optimization problem. We are given a set of points in the plane and we are asked to find k points such that among these k points, the shortest distance is maximized. This problem is shown to be NP-complete by Wang and Kuo (1988). Try to develop an approximation algorithm to solve this problem.

Nov 29 2021

Let there be a set of points densely distributed on a circle. Apply the approximation Euclidean traveling salesperson algorithm to find an approximate tour for this set of points. Is this result also an optimal one? Consider the four points on a square as shown below. Solve the bottleneck traveling salesperson problem approximately by the algorithm introduced in this chapter. Is the result...

Nov 29 2021

Show that there does not exist any polynomial time approximation algorithm for the traveling salesperson problem such that the error caused by the approximation algorithm is bounded within · TSP where is any constant and TSP denotes an optimal solution. (Hint: Show that the Hamiltonian cycle problem can be reduced to this problem.) Apply an approximation convex hull algorithm to find an...

Nov 29 2021

- Programming Languages
- Automata or Computationing
- Database Management System
- Computer Architecture
- Networking
- Computer Graphics and Multimedia Applications
- Operating System
- Information Technology
- Data Structures
- Software Engineering
- Computer Network Security
- Linux Environment
- Computer Science - Others
- Programming In Java
- Programming In C/C++
- Programming In Python
- SQL/PSQL
- Network Management Security
- Programming In Assembly Language
- System Design
- Cryptography
- Software Project Management Concepts
- Software Design
- Internet Programming
- Data Link Control Protocols
- LINUX
- Network Topologies
- Programming In .NET
- Artificial Intelligence
- Dynamic Programming
- UNIX
- Oracle
- Compilers