In this paper we show that conditional graph entropy can be formulated as an alternating minimization problem, which gives rise to a simple iterative algorithm for numerically computing (conditional) graph entropy. The systematic study of alternating minimization problems was initiated by Csisz\'ar and Tusn\'ady. We apply this theory to conditional graph entropy, which was shown to be the minimal rate for a natural functional compression problem with side information at the receiver. 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.

翻译：本文中我们显示, 有条件的图形 entropy 可以作为一个交替最小化问题来配制, 从而产生一个简单的迭代算法来进行数字计算( 有条件的) 图形 entropy 。 对交替最小化问题的系统研究是由 Csisz\'ar 和 Tusn\'ady 启动的。 我们把这个理论应用到有条件的图形 entropy 上, 这被证明是接收器侧边信息中自然功能压缩问题的最低速率 。 这还导致一个新的公式, 显示有条件的图形 entropy 是更一般性框架的一部分 : comvex 角上优化问题的解决方案 。 在图形 entropy ( 即不附带条件的版本) 的特殊案例中, 这是由 Csisz\\ ar, K\\\ “ orner, Lov\' as, Marton, 和 Simony 所为人所知的 。 在这种情况下, comvex 角落的作用是由所谓的顶点包装聚点所扮演的。 在 。 在 有条件的版本中, 它是一个更复杂的 convevex botion 。