Ogden, Robert D.2011-02-082012-02-242011-01Ogden, R. D. (2011). Coverings of finite sets by random covers, with applications to the HELP protocol (Report No. TXSTATE-CS-TR-2011-28). Texas State University-San Marcos, Department of Computer Science.https://hdl.handle.net/10877/2593If we choose subsets of a finite set s at random, according to some specified distribution, how many subsets have to be chosen until s is covered? We solve this problem for distributions invariant under permutations of s by a Markov chain model and derive a useful estimate for a sufficient number of subsets to form a cover with a specified probability. These results are applied to the HELP network protocol [GGO] to estimate the number of times the server must send a set of file fragments to clients, not all of them helpful, in order to ensure that all the fragments be shared.Text9 pages1 file (.pdf)enHELP protocolserversMarkov chain modelComputer ScienceReport