# Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

__Mittagsseminar Talk Information__ | |

**Date and Time**: Thursday, July 21, 2005, 12:15 pm

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

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

**Speaker**: Masashi Kiyomi (National Institute of Informatics (NII)

## Efficient Algorithms for the Electric Power Transaction Problem

We present two efficient algorithms for solving the electric power
transaction problem. The electric power transaction problem appears
when maximizing the social benefit on electric power transactions
between some companies. The problem is a special case of the minimum
cost flow problem; on a network with few vertices with degrees at
least two, and many vertices with degrees one. Our first algorithm is
based on the minimum cycle canceling algorithm and the second
algorithm uses a linear time median finding algorithm. On a network
having *n* vertices with *k* vertices of degrees more than one, the
first algorithm finds an optimal solution in *O(n log
n k*^{6} log(kC)) time, where *C* is the highest electric power price
per unit that the companies may offer. The second algorithm takes
*O((n+k*^{4})2^{k}k!) time, which is linear in *n*. In practice, *k* is small and *n* is very large, hence these algorithms are efficient
compared to the other network flow algorithms.

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