Combinatorial property testing (a survey)
Combinatorial property testing (a survey)
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组合属性测试（调查）
DOI：
10.1090/dimacs/043/04
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发表时间：
1997
期刊：
影响因子：
--
通讯作者：
Oded Goldreich
中科院分区：
文献类型：
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作者：
Oded Goldreich
我们考虑的问题，确定是否一个给定的对象有一个预定的属性或“远离”任何对象具有该属性。特别地，对象由函数建模，并且函数之间的距离被测量为函数在其上消失的域的分数。我们考虑（随机）算法，可以查询的功能，在他们选择的参数，并寻求算法查询的功能在相对较少的地方。我们专注于组合性质，特别是在图形属性。图的两种标准表示（邻接矩阵和关联表）产生了两种不同的测试图性质的模型。在最适合稠密图的rst模型中，N-顶点图之间的距离被测量为图在N 2上不一致的边的分数。在第二个模型中，最适合于有界度图，N顶点d度图之间的距离被测量为图在dN上不一致的边的分数。为了说明这两个模型，我们调查结果的复杂性测试图是否二分。对于一个常数的距离参数，一个常数数量的查询suuce在第一个模型，而e（p N）查询是必要的和suucient在第二个模型。
We consider the question of determining whether a given object has a predetermined property or is \far" from any object having the property. Speciically, objects are modeled by functions, and distance between functions is measured as the fraction of the domain on which the functions diier. We consider (randomized) algorithms which may query the function at arguments of their choice, and seek algorithms which query the function at relatively few places. We focus on combinatorial properties, and speciically on graph properties. The two standard representations of graphs { by adjacency matrices and by incidence lists { yield two diierent models for testing graph properties. In the rst model, most appropriate for dense graphs, distance between N-vertex graphs is measured as the fraction of edges on which the graphs disagree over N 2. In the second model, most appropriate for bounded-degree graphs, distance between N-vertex d-degree graphs is measured as the fraction of edges on which the graphs disagree over dN. To illustrate the two models, we survey results regarding the complexity of testing whether a graph is Bipartite. For a constant distance parameter, a constant number of queries suuce in the rst model, whereas e (p N) queries are necessary and suucient in the second model.