AI 中文总结
本文研究度序列优化问题在二次函数下的复杂度，引入图的临界根概念，证明该问题最优值随二次根变化的区间为凸分段仿射函数。
AI 中文摘要
度序列优化问题是在给定图中寻找一个子图，使得该子图各顶点的度对应的给定函数之和最大。本文研究该问题及其在二次函数下的复杂度，特别引入图的临界根概念，并证明当二次根变化时，该问题的最优值所定义的区间为凸分段仿射函数。
英文摘要
The degree sequence optimization problem is to find a subgraph of a given graph which maximizes the sum over all vertices of a given function evaluated at the subgraph degree of that vertex. Here we study this problem and its complexity for quadratic functions. In particular, we introduce the critical roots of a graph, and show they define intervals over which the optimal value of the problem, as the quadratic root varies, is convex piecewise affine.
