Communication complexity and data compression

U. Tamm
2013 2013 Information Theory and Applications Workshop (ITA)  
A result of Ahlswede and Cai for the 2-party communication complexity of set intersection is generalized to a multiparty model. There are relations to several areas as to the direct-sum conjecture and amortized complexity in computational complexity or interactive communication in information theory as well as to wireless sensor networks and even quantum communication. The aim of the paper is mostly to survey these different applications and to draw the attention of researchers in one area to
more » ... e results and applications in other areas. Index Terms-prefix codes, communication complexity, amortized complexity, functions on direct sums forehead" model in which each person knows all inputs but her own, for instance [7] or [22] . The "number in hand" model, in which each person knows just her own input, was not so popular in the beginning but later found an important application in streaming [5] . So it was natural to extend set interesection and other functions defined over the binary alphabet to more than 2 arguments. The compression for set intersection also was helpful in the study of several more functions. Whereas the direct -sum conjecture states that a significant reduction of communication cannot be expected by increasing the length n of the inputs, set intersection demonstrates that the amount of communication can significantly be reduced, when the number k of communicators is increased. This has an application in wireless sensor networks. Observe that the naive protocol would require n · k bits of communication among the k communicators, whereas the compressed protocol above requires only n · log 2 (k + 1) bits. Kowshik and Kumar in [14] were interested in this reduction of communication and derived a more general result for threshold functions, where set intersection occurs as a special case. Thus, instead of calculating the basic function at every time instance separately, the sensor network can save energy by collecting information about n time instances and then follow the compressed protocol.
doi:10.1109/ita.2013.6502978 dblp:conf/ita/Tamm13a fatcat:n5ozduopi5h3reyh6gilobfvx4