Title :
Multi-Session Function Computation and Multicasting in Undirected Graphs
Author :
Kannan, S. ; Viswanath, Pramod
Author_Institution :
Dept. of EECS, Univ. of California, Berkeley, Berkeley, CA, USA
Abstract :
In the function computation problem, certain nodes of an undirected graph have access to independent data, while some other nodes of the graph require certain functions of the data; this model, motivated by sensor networks and cloud computing, is the focus of this paper. We study the maximum rates at which function computation is possible on a capacitated graph; the capacities on the edges of the graph impose constraints on the communication rate. We consider a simple class of computation strategies based on Steiner-tree packing (so-called computation trees), which does not involve block coding and has minimal delay. With a single terminal requiring function computation, computation trees are known to be optimal when the underlying graph is itself a directed tree, but have arbitrarily poor performance in general directed graphs. Our main result is that computation trees are near optimal for a wide class of function computation requirements even at multiple terminals in undirected graphs. The key technical contribution involves connecting approximation algorithms for Steiner cuts in undirected graphs to the function computation problem. Furthermore, we show that existing algorithms for Steiner tree packings allow us to compute approximately optimal packings of computation trees in polynomial time. We also show a close connection between the function computation problem and a communication problem involving multiple multicasts.
Keywords :
approximation theory; block codes; cloud computing; computational complexity; directed graphs; multicast communication; telecommunication computing; trees (mathematics); wireless sensor networks; Steiner cuts; Steiner tree packings; Steiner-tree packing; approximation algorithms; block coding; capacitated graph; cloud computing; communication rate; computation strategy; computation trees; directed tree; function computation problem; function computation requirements; general directed graphs; minimal delay; multicasting; multiple multicasts; multisession function computation; optimal packings; polynomial time; sensor networks; single terminal; undirected graphs; Approximation algorithms; Encoding; Histograms; Multicast communication; Network coding; Steiner trees; Unicast; Function computation; Steiner packing; capacity; computation trees; multicasting; multiple unicast; network coding; sensor networks;
Journal_Title :
Selected Areas in Communications, IEEE Journal on
DOI :
10.1109/JSAC.2013.130408