The Information Flow Problem on Clock Networks

Abstract. The information flow problem on a network asks whether r senders, v1, v2, . . . , vr can each send messages to r corresponding receivers vn+1, . . . , vn+r via intermediate nodes vr+1, . . . , vn. For a given finite R ⊂ Z, the clock network Nn(R) has edge vivk if and only if k > r and k−i ∈ R. We show that the information flow problem on Nn({1, 2, . . . , r}) can be solved for all n ≥ r. We also show that for any finite R such that gcd(R) = 1 and r = max(R), we show that the information flow problem can be solved on Nn(R) for all n ≥ 3r . This is an improvement on the bound given in [10] and answers an open question from [9].