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1 2 2 1 2 1 5 1 3 100 5 4 1 z* ≥ z(Î*) + Σ λ; (d¿(γ) − 2) iЄN -

1 2 2 1 2 1 5 1 3 100 5 4 1 z* ≥ z(Î*) + Σ λ; (d¿(γ) − 2) iЄN -

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Question

Consider the network in the following figure. Edges that are not pictured have a length of ∞.

Image attatched

(a) What is the optimal TSP tour on this network, and what is its total length, z*? What is the optimal 1-tree Tˆ* on this network (“rooted” at node 1), and what is its total length, z(Tˆ*)?

(b) Find the best Held-Karp lower bound you can. That is, find weights to add to one or more nodes so that z* and the right-hand side of the following formula are as close as possible.

z* ≥ z(Tˆ*) + SUM{i∈N}  λi(di(Tˆ*) − 2)     Image attatched

Here Tˆ* is the optimal 1-tree under the revised distance matrix, z(Tˆ*) is its cost and di(Tˆ*) is the degree of node i in 1-tree Tˆ*.

1 2 2 1 2 1 5 1 3 100 5 4 1 z* ≥ z(Î*) + Σ λ; (d¿(γ) − 2) iЄN -
Transcribed Image Text:1 2 2 1 2 1 5 1 3 100 5 4 1 z* ≥ z(Î*) + Σ λ; (d¿(γ) − 2) iЄN -
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