Conditional graph entropy is known to be the minimal rate for a natural functional compression problem with side information at the receiver. In this paper we show that it can be formulated as an alternating minimization problem, which gives rise to a simple iterative algorithm for numerically computing (conditional) graph entropy. This also leads to a new formula which shows that conditional graph entropy is part of a more general framework: the solution of an optimization problem over a convex corner. In the special case of graph entropy (i.e., unconditioned version) this was known due to Csisz\'ar, K\"orner, Lov\'asz, Marton, and Simonyi. In that case the role of the convex corner was played by the so-called vertex packing polytope. In the conditional version it is a more intricate convex body but the function to minimize is the same. Furthermore, we describe a dual problem that leads to an optimality check and an error bound for the iterative algorithm.

翻译：条件图熵已知是接收端具有边信息的自然函数压缩问题的最小速率。本文表明，它可以表述为交替最小化问题，从而产生一种用于数值计算（条件）图熵的简单迭代算法。这也引出了一个新公式，表明条件图熵是更一般框架的一部分：凸角上优化问题的解。在图熵（即无条件版本）的特殊情况下，这一点因Csiszár、Körner、Lovász、Marton和Simonyi的工作而为人所知。在该情况下，凸角的作用由所谓的顶点包装多面体扮演。在条件版本中，它是一个更复杂的凸体，但待最小化的函数相同。此外，我们描述了一个对偶问题，该问题为迭代算法提供了最优性检验和误差界。