# Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

__Mittagsseminar Talk Information__ | |

**Date and Time**: Tuesday, March 22, 2005, 12:15 pm

**Duration**: This information is not available in the database

**Location**: This information is not available in the database

**Speaker**: Shankar Ram Lakshminarayanan

## Metric Traveling Salesman Games

The Traveling Salesman game is given by the tuple *(N, c*_{D}) where
*N* is the set of cities (or the vertices of the complete graph)
and *c*_{D} is a real function defined on all subsets of *N* where
*D* is the underlying cost matrix, with *c*_{D}(S) being the cost of a minimum
cost Hamiltonian tour through the vertices *S* and "0" where
*0 ∉ N* is called as the home city. The core of this game
is defined to be the set of all *n*-dimensional real vectors *x*, such
that *x(N) = c*_{D}(N) and *x(S) <= c*_{D}(S) for all subsets *S*. In this
talk, we show that the problem of determining whether the core of
a TS game with *D* satisfying triangle inequality (Metric TS game) is
empty or not, is *NP*-Complete. Further, we define approximate core
allocation and show some results pertaining to the Asymmetric TS game.

(Joint work with Markus Bläser)

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