{"references": ["Pascal Frossard Antonio Ortega David I Shuman, Sunil K. Narang and\nPierre Vandergheynst, \"The emerging field of signal processing on\ngraphs,\" IEEE Signal Processing Magazine, pp. 83\u201398, May 2013.", "Jose M. F. Moura Aliaksei Sandryhaila, \"Discrete signal processing\non graphs,\" IEEE Transactions on Signal Processing, vol. 61, pp.\n1644\u20131656, 2013.", "F. R. K. Chung, Spectral Graph Theory, AMS, 1996.", "P. Vandergheynst D. K. Hammond and R. Gribonval, \"Wavelets on\ngraphs via spectral graph theory,\" J. Appl. Comp. Harm. Anal, vol. 30,\nno. 2, pp. 129150, 2011.", "Markus P\u00a8uschel and Jos\u00b4e M. F. Moura, \"Algebraic signal processing\ntheory: Foundation and 1-D time,\" IEEE Transactions on Signal\nProcessing, vol. 56, no. 8, pp. 3572\u20133585, 2008.", "Markus P\u00a8uschel and Jos\u00b4e M. F. Moura, \"Algebraic signal processing\ntheory: 1-D space,\" IEEE Transactions on Signal Processing, vol. 56,\nno. 8, pp. 3586\u20133599, 2008.", "A. Sandryhaila and J. M. F. Moura, \"Discrete signal processing on\ngraphs: Graph fourier transform,\" in IEEE International Conference\non Acoustics, Speech, and Signal Processing (ICASSP), pp. 6167-6170,\n2013.", "J. M. F. Moura A. Sandryhaila, \"Discrete signal processing on graphs:\nGraph filters,\" in IEEE International Conference on Acoustics, Speech,\nand Signal Processing (ICASSP), pp. 6163-6166, 2013.", "J. M. F. Moura A. Sandryhaila, \"Discrete signal processing on graphs:\nFrequency analysis,\" IEEE Transactions on Signal Processing, vol. 62,\nno. 12, pp. 3042\u20133054, 2014.\n[10] P. Lancaster and M. Tismenetsky, The Theory of Matrices, Academic\nPress, 2nd edition, 1985.\n[11] Jose M. F. Moura Jelena Kovacevic Siheng Chen, Aliaksei Sandryhaila,\n\"Signal denoising on graphs via graph filtering,\" in IEEE Global\nConference on Signal and Information Processing (GlobalSIP),,\nDecember 2014.\n[12] Kang-Pu Paul Liu Alex Pothen, Horst D. Simon, \"Partitioning sparse\nmatrices with eigenvectors of graphs,\" Report, NAS Systems Division,\nNASA Ames Research Center, 1989."]}

An algebraic framework for processing graph signals axiomatically designates the graph adjacency matrix as the shift operator. In this setup, we often encounter a problem wherein we know the filtered output and the filter coefficients, and need to find out the input graph signal. Solution to this problem using direct approach requires O(N3) operations, where N is the number of vertices in graph. In this paper, we adapt the spectral graph partitioning method for partitioning of graphs and use it to reduce the computational cost of the filtering problem. We use the example of denoising of the temperature data to illustrate the efficacy of the approach.