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| Content Provider | IEEE Xplore Digital Library |
|---|---|
| Author | Feizi, S. Médard, M. |
| Copyright Year | 2010 |
| Description | Author affiliation: RLE at MIT, USA (Feizi, S.; Médard, M.) |
| Abstract | In this paper, we consider the problem of finding the minimum entropy coloring of a characteristic graph under some conditions which allow it to be in polynomial time. This problem arises in the functional compression problem where the computation of a function of sources is desired at the receiver. The rate region of the functional compression problem has been considered in some references under some assumptions. Recently, Feizi et al. computed this rate region for a general one-stage tree network and its extension to a general tree network. In their proposed coding scheme, one needs to compute the minimum entropy coloring (a coloring random variable which minimizes the entropy) of a characteristic graph. In general, finding this coloring is an NP-hard problem (as shown by Cardinal et al.). However, in this paper, we show that depending on the characteristic graph's structure, there are some interesting cases where finding the minimum entropy coloring is not NP-hard, but tractable and practical. In one of these cases, we show that, having a non-zero joint probability condition on RVs' distributions, for any desired function f, makes characteristic graphs to be formed of some non-overlapping fully-connected maximal independent sets. Therefore, the minimum entropy coloring can be solved in polynomial time. In another case, we show that if f is a quantization function, this problem is also tractable. |
| Starting Page | 116 |
| Ending Page | 120 |
| File Size | 139242 |
| Page Count | 5 |
| File Format | |
| ISBN | 9781424478903 |
| e-ISBN | 9781424478927 |
| e-ISBN | 9781424478910 |
| DOI | 10.1109/ISIT.2010.5513270 |
| Language | English |
| Publisher | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher Date | 2010-06-13 |
| Publisher Place | USA |
| Access Restriction | Subscribed |
| Rights Holder | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subject Keyword | Entropy Polynomials Computer networks Tree graphs Random variables NP-hard problem Quantization Probability distribution graph entropy Functional compression graph coloring |
| Content Type | Text |
| Resource Type | Article |
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