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Summary: Almost two decades ago Ahlswede introduced an abstract correlated source \(({\mathcal V}\times{\mathcal W},{\mathcal S})\) with outputs \((v,w)\in{\mathcal S}\subset{\mathcal V}\times{\mathcal W}\), where persons \(P_{\mathcal V}\) and \(P_{\mathcal W}\) observe \(v\) and \(w\), respectively. More recently, Orlitsky considered the minimal number \(C_m\) of bits to be transmitted in \(m\) rounds to ``inform \(P_{\mathcal W}\) about \(v\) over one channel.'' He showed that \(C_2\leq 4C_\infty+3\) and that in general \(C_2\nsim C_\infty\). We give a simple example for \(C_3\nsim C_\infty\). However, for the new model ``inform \(P_{\mathcal W}\) over two channels,'' four rounds are optimal for this example -- a result we conjecture in general. If both \(P_{\mathcal V}\) and \(P_{\mathcal W}\) are to be informed over two channels about the other outcome, we determine asymptotically the complexities for all sources. In our last model ``inform \(P_{\mathcal V}\) and \(P_{\mathcal W}\) over one channel'' for all sources the total number \(T_2\) of required bits is known asymptotically and \(T_\infty\) is bounded from below in terms of average degrees. There are exact results for several classes of regular sources. An attempt is made to discuss the methods of the subject systematically.
hypergraph covering and, Communication theory, average degree bound, abstract sources, Source coding, Hypergraphs, worst case complexity, hypergraph covering and coloring, communication complexity, coloring
hypergraph covering and, Communication theory, average degree bound, abstract sources, Source coding, Hypergraphs, worst case complexity, hypergraph covering and coloring, communication complexity, coloring
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 12 | |
popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Average | |
influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Top 10% | |
impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Average |