Optimal Skewed Allocation on Multiple Channels for Broadcast in Smart Cities

We consider the problem of allocating N uniform data to K transmission channels so as the average Expected Delay (AED) is minimized. This problem arises in designing efficient data-diffusion broadcast algorithms in a smart environment. We show that the basic dynamic rogramming algorithm for solving the uniform pallocation problem can be speedup up to O(NK) time by applying an optimal algorithm to find the row-minima of totally monotone matrices. Such a new algorithm is always faster than the best previously known algorithm for the uniform allocation problem that runs in O(NKlogN). Moreover, it is computationally optimal for the uniform allocation of up to N data and K channels. We then reduce the largest allocation problem, i.e., the subproblem with exactly N data and K channels, to the problem of finding a minimum weight K-link path in a particular directed acyclic graph. We also present two heuristics and we show by extended simulations their effectiveness in practical scenarios. Both the K-link path algorithm and the heuristics are much faster than O(NK). We then compare the behaviours of our algorithms on the online version of the allocation problem in which new single items are inserted for broadcast.

[1]  Paolo Ferragina,et al.  Distribution-Aware Compressed Full-Text Indexes , 2011, Algorithmica.

[2]  George Kingsley Zipf,et al.  Human behavior and the principle of least effort , 1949 .

[3]  Shamkant B. Navathe,et al.  Efficient Data Allocation over Multiple Channels at Broadcast Servers , 2002, IEEE Trans. Computers.

[4]  Li Fan,et al.  Web caching and Zipf-like distributions: evidence and implications , 1999, IEEE INFOCOM '99. Conference on Computer Communications. Proceedings. Eighteenth Annual Joint Conference of the IEEE Computer and Communications Societies. The Future is Now (Cat. No.99CH36320).

[5]  Yan Shi,et al.  Efficient data retrieval scheduling for multi-channel wireless data broadcast , 2012, 2012 Proceedings IEEE INFOCOM.

[6]  Klaas Willems,et al.  George Kingsley Zipf , 2006 .

[7]  Alan A. Bertossi,et al.  Optimal skewed data allocation on multiple channels with flat broadcast per channel , 2005, IEEE Transactions on Computers.

[8]  Sungwon Jung,et al.  Effective Generation of Data Broadcast Schedules with Different Allocation Numbers for Multiple Wireless Channels , 2008, IEEE Transactions on Knowledge and Data Engineering.

[9]  Alok Aggarwal,et al.  Finding a minimum-weightk-link path in graphs with the concave Monge property and applications , 1994, Discret. Comput. Geom..

[10]  Alok Aggarwal,et al.  Finding a minimum weight K-link path in graphs with Monge property and applications , 1993, SCG '93.

[11]  Baruch Schieber,et al.  Computing a minimum-weight k-link path in graphs with the concave Monge property , 1995, SODA '95.

[12]  Lawrence L. Larmore,et al.  The Knuth-Yao quadrangle-inequality speedup is a consequence of total-monotonicity , 2009, SODA '06.

[13]  Rainer E. Burkard,et al.  Perspectives of Monge Properties in Optimization , 1996, Discret. Appl. Math..

[14]  Alok Aggarwal,et al.  Geometric applications of a matrix-searching algorithm , 1987, SCG '86.