What question did this study set out to answer?

To formulate a relaxed, global notion of metric dimension and establish efficient approximation schemes for the traveling salesman problem on spaces with dense regions that remain well-behaved on average.

January 20, 2008

Approximating TSP on metrics with bounded global growth

View Full Paper

Ask AI

Bookmark

Authors

TCT-H. Hubert ChanChinese University of Hong Kong AGAnupam GuptaSiddhartha Medical College

Discussion

Member takes

Implication

Theoretical analysis reveals subexponential approximation algorithms for traveling salesman problems under bounded correlation dimensions, indicating broader tractability beyond doubling metrics.

Key Points

To formulate a relaxed, global notion of metric dimension and establish efficient approximation schemes for the traveling salesman problem on spaces with dense regions that remain well-behaved on average.
Introduced correlation dimension as a global metric dimension generalizing doubling dimension to accommodate uniform submetrics of size up to the square root of n.
Formulated an exact algorithm using local structural arguments and a polynomial-time approximation framework using the global metric properties.
Demonstrated exact solvability of the traveling salesman problem in 2^O(√n) time on metrics with constant correlation dimension.
Developed a (1 + ε)-approximation algorithm running in sub-exponential time (2^O(n^Δ · ε^-4dimC)) for any constant 0 < Δ < 1.

Cite This Study

Chan et al. (2008) studied this question.

synapsesocial.com/papers/6a0ec4067046b28dbef9a315 https://doi.org/10.1145/1347082.1347158

View Full Paper

Ask AI

Bookmark

Implication

Theoretical analysis reveals subexponential approximation algorithms for traveling salesman problems under bounded correlation dimensions, indicating broader tractability beyond doubling metrics.

Approximating TSP on metrics with bounded global growth

Discussion

Member takes

Implication

Key Points

Cite This Study

Approximating TSP on metrics with bounded global growth

Discussion

Member takes

Implication

Key Points

Cite This Study

Also Consider

Also Consider