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• W3104225535 abstract "In discrete optimization, representing an objective function as an $s$-$t$ cut function of a network is a basic technique to design an efficient minimization algorithm. A network representable function can be minimized by computing a minimum $s$-$t$ cut of a directed network, which is a very easy and fastly solved problem. Hence it is natural to ask what functions are network representable. In the case of pseudo Boolean functions (functions on ${0,1}^n$), it is known that any submodular function on ${0,1}^3$ is network representable. v{Z}ivn'y--Cohen--Jeavons showed by using the theory of expressive power that a certain submodular function on ${0,1}^4$ is not network representable. In this paper, we introduce a general framework for the network representability of functions on $D^n$, where $D$ is an arbitrary finite set. We completely characterize network representable functions on ${0,1}^n$ in our new definition. We can apply the expressive power theory to the network representability in the proposed definition. We prove that some ternary bisubmodular function and some binary $k$-submodular function are not network representable." @default.
• W3104225535 created "2020-11-23" @default.
• W3104225535 creator A5002829682 @default.
• W3104225535 date "2017-05-20" @default.
• W3104225535 modified "2023-10-04" @default.
• W3104225535 title "On a general framework for network representability in discrete optimization" @default.
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• W3104225535 doi "https://doi.org/10.1007/s10878-017-0136-y" @default.
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