非线性规划的多项式核：覆盖、填充和可行性
On Polynomial Kernels for Integer Linear Programs: Covering, Packing and Feasibility
摘要：
本文研究了整数线性规划的可行性判定问题，以及寻找覆盖和填充整数线性规划的好解问题的多项式核的存在性。我们的主要结果如下：首先，我们表明，ILP可行性问题承认没有多项式核化时，参数化的变量和约束的数量，除非NP \subseteq coNP/聚。这扩展到有限的情况下，有界变量的程度和有限数量的变量，每个约束，并覆盖和包装的ILP。其次，我们给出了覆盖ILP问题的多项式核化，当A是行稀疏的时，要求解Ax >= b，c^Tx <= k，由k参数化;这推广了具有0/1-变量和系数的特殊情况（d-命中集）的已知多项式核化。
英文摘要：
We study the existence of polynomial kernels for the problem of deciding feasibility of integer linear programs (ILPs), and for finding good solutions for covering and packing ILPs. Our main results are as follows: First, we show that the ILP Feasibility problem admits no polynomial kernelization when parameterized by both the number of variables and the number of constraints, unless NP \subseteq coNP/poly. This extends to the restricted cases of bounded variable degree and bounded number of variables per constraint, and to covering and packing ILPs. Second, we give a polynomial kernelization for the Cover ILP problem, asking for a solution to Ax >= b with c^Tx <= k, parameterized by k, when A is row-sparse; this generalizes a known polynomial kernelization for the special case with 0/1-variables and coefficients (d-Hitting Set).
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