Solution to Exchanges 9.1 Puzzle: Borrowing as Cheaply as Possible NIKOS KARANIKOLAS and MARIA KYROPOULOU University of Patras, Greece and TROELS BJERRE SÃRENSEN University of Warwick, United Kingdom This is a solution to the Editor s Puzzle published in Issue 9.1 of SIGecom Exchanges [Conitzer 2010]. The puzzle is about nding the least expensive way for a player to borrow a certain amount of money from others under some given constraints and can be found at http://www.sigecom.org/exchanges/volume 9/1/puzzle.pdf. 1. THE MODEL This problem can be easily modeled as an instance of the minimum cost ow problem. In this problem, we are given a directed graph G = (V, E) (or network), where each node is associated with a demand value, and each arc is characterized by two non-negative values denoting its cost and capacity. The goal is to regulate the ow of a single commodity in the network in a way that satis es all demands, minimizes the cost, and obeys the capacity constraints of each edge. The instance is depicted in Figure 1(a). Each person is represented by a node. Speci cally, nodes A, B, D, E, G, H and Z correspond to Alice, Bob, Denise, Ed,
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Solution to Exchanges 9.1 puzzle: borrowing as cheaply as possible
Karanikolas, Nikos; Kyropoulou, Maria; Sørensen, Troels Bjerre
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, Volume 10 (2)
Association for Computing Machinery – Jun 1, 2011
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