The median function on trees. (English) Zbl 1280.05021
Summary: A median of a sequence \(\pi = (x_{1}, x_{2}, \ldots, x_{k})\) of elements of a finite metric space \((X, d)\) is an element \(x\) for which \(\sum^k_{i=1} d(x,x_i)\) is minimum. The function with domain the set of all finite sequences on \(X\) and defined by \(\operatorname{Med}(\pi) = \{x \mid x \text{ is a median of }\pi\}\) is called the median function on \(X\). In this note, an axiomatic characterization of the median function on finite trees is given.
MSC:
| 05C05 | Trees |
| 05C12 | Distance in graphs |
| 68R10 | Graph theory (including graph drawing) in computer science |
| 90B80 | Discrete location and assignment |
| 94C15 | Applications of graph theory to circuits and networks |
References:
| [1] | Arrow K. J., Handbook of Social Choice and Welfare 1 (2002) · Zbl 1307.91009 |
| [2] | Arrow K. J., Handbook of Social Choice and Welfare 2 (2005) |
| [3] | DOI: 10.1137/0404028 · Zbl 0734.90008 · doi:10.1137/0404028 |
| [4] | DOI: 10.1016/0165-4896(81)90041-X · Zbl 0486.62057 · doi:10.1016/0165-4896(81)90041-X |
| [5] | Day W. H. E., Frontiers in Appl. Math 29 (2003) |
| [6] | DOI: 10.1287/opre.46.3.347 · Zbl 0979.90118 · doi:10.1287/opre.46.3.347 |
| [7] | DOI: 10.1287/moor.15.3.553 · Zbl 0715.90070 · doi:10.1287/moor.15.3.553 |
| [8] | DOI: 10.1142/S1793830910000681 · Zbl 1226.05087 · doi:10.1142/S1793830910000681 |
| [9] | McMorris F. R., Networks 60 pp 94– |
| [10] | DOI: 10.1016/S0166-218X(02)00213-5 · Zbl 1026.06007 · doi:10.1016/S0166-218X(02)00213-5 |
| [11] | DOI: 10.1016/S0166-218X(98)00003-1 · Zbl 0906.05023 · doi:10.1016/S0166-218X(98)00003-1 |
| [12] | DOI: 10.1002/net.1027 · Zbl 0990.90063 · doi:10.1002/net.1027 |
| [13] | Mirchandani P. B., Discrete Location Theory (1990) · Zbl 0718.00021 |
| [14] | Mulder H. M., Australasian J. Combinatorics 41 pp 223– |
| [15] | DOI: 10.1016/0377-2217(94)00330-0 · Zbl 0914.90182 · doi:10.1016/0377-2217(94)00330-0 |
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