Finding Stable Matchings that are Robust to Errors in the Input
Finding Stable Matchings that are Robust to Errors in the Input
复制标题
寻找对输入中的错误具有鲁棒性的稳定匹配
DOI：
10.4230/lipics.esa.2018.60
复制
发表时间：
2018
影响因子：
1.2
通讯作者：
V. Vazirani
中科院分区：
文献类型：
--
作者：
Tung Mai;V. Vazirani
我们研究了找到稳定匹配问题的解决方案的问题，这些解决方案对输入中的错误是可靠的，并且我们获得了特殊类别错误类别的多项式时间算法。在此过程中，我们还提出了有关稳定匹配问题的新结构问题的工作，即发现两个“附近”实例解决方案的晶格之间的关系。
我们的主要算法结果是：我们确定了一个多个多项式的错误类别，$ d $，可以在稳定的匹配实例中引入。给定实例$ a $稳定匹配，让$ b $为随机变量，代表从$ d $引入{\ em One}错误后结果的实例，这是通过给定的离散概率分发选择的。问题是要找到$ a $的稳定匹配，以最大化$ b $稳定的可能性。通过上述问题中描述的类型的新结构特性，我们为此问题提供了一个组合多项式时间算法。
我们还表明，在概率分配$ p $下，例如$ a $的一组健壮的稳定匹配，形成了$ a $的稳定匹配晶格的sublattice。我们给出了一种有效的算法来找到该集合的简洁表示。该表示的属性是该集合的任何成员都可以从中有效检索。
We study the problem of finding solutions to the stable matching problem that are robust to errors in the input and we obtain a polynomial time algorithm for a special class of errors. In the process, we also initiate work on a new structural question concerning the stable matching problem, namely finding relationships between the lattices of solutions of two "nearby" instances.
Our main algorithmic result is the following: We identify a polynomially large class of errors, $D$, that can be introduced in a stable matching instance. Given an instance $A$ of stable matching, let $B$ be the random variable that represents the instance that results after introducing {\em one} error from $D$, chosen via a given discrete probability distribution. The problem is to find a stable matching for $A$ that maximizes the probability of being stable for $B$ as well. Via new structural properties of the type described in the question stated above, we give a combinatorial polynomial time algorithm for this problem.
We also show that the set of robust stable matchings for instance $A$, under probability distribution $p$, forms a sublattice of the lattice of stable matchings for $A$. We give an efficient algorithm for finding a succinct representation for this set; this representation has the property that any member of the set can be efficiently retrieved from it.
影响因子：
1.1
作者：
H. Aziz;P. Biró;Serge Gaspers;Ronald de Haan;Nicholas Mattei;Baharak Rastegari
通讯作者：
H. Aziz;P. Biró;Serge Gaspers;Ronald de Haan;Nicholas Mattei;Baharak Rastegari