如何解决在 jqwik 属性测试框架中寻找更好的方法来生成图的边列表
目前我正在使用:
@Provide
Arbitrary<List<Tuple.Tuple3<Integer,Integer,Integer>>> edgeLists (
TypeUsage type,ArbitraryProvider.SubtypeProvider subtype) {
int vertices = 10;
int degree_min = 1;
int degree_max = 4;
int min_edge_flow = 1;
int max_edge_flow = 10;
for (Annotation a : type.getAnnotations()) {
if (a instanceof MaxFlowParameters) {
MaxFlowParameters params = (MaxFlowParameters) a;
vertices = Math.max(1,params.vertices());
degree_min = Math.max(1,params.degree_min());
degree_max = Math.min(vertices,Math.max(degree_min,params.degree_max()));
min_edge_flow = Math.min(vertices,Math.max(0,params.min_edge_flow()));
max_edge_flow = Math.min(vertices,Math.max(min_edge_flow,params.max_edge_flow()));
}
}
Function<List<Integer>,List<Integer>> expand = new Function<List<Integer>,List<Integer>> () {
@Override
public List<Integer> apply (List<Integer> t) {
List<Integer> result = new ArrayList<>();
ListUtils.enumerate(t,(idx,copies) -> {
while (copies-- > 0) result.add(idx+1);
return true;
});
return result;
}
};
int num_vertices = vertices;
int the_min_edge_flow = min_edge_flow;
int the_max_edge_flow = max_edge_flow;
return Arbitraries.integers().between(degree_min,degree_max).list().ofSize(vertices).map(expand)
.flatMap(sources -> Arbitraries.integers().between(1,num_vertices).list().ofSize(sources.size())
.flatMap(targets -> Arbitraries.integers().between(the_min_edge_flow,the_max_edge_flow).list().ofSize(sources.size())
.map(flows -> {
int limit = sources.size();
List<Tuple3<Integer,Integer>> result = new ArrayList<>(limit);
for (int i = 0; i < limit; i++) {
result.add(Tuple.of(sources.get(i),targets.get(i),flows.get(i)));
}
return result;
})));
}
@Provide
Arbitrary<Graph<String,IntegerFlow>> graphs (TypeUsage type,ArbitraryProvider.SubtypeProvider subtype) {
return Combinators.withBuilder(() -> new GraphBuilder())
.use(this.edgeLists(type,subtype)).in((builder,edges) -> builder.withEdges(edges))
.build(builder -> builder.build());
}
@Property
void searchOrdersEqual (
@ForAll @From("edgeLists") List<Tuple.Tuple3<Integer,Integer>> edgeList,@ForAll Random random) {
// for current in memory graph impl the search order in which augmenting paths are found will change
// if the order the edges are declared in changes. so if we see that one search order does not
// yield the same result as another,that the algo can not always be finding the max flow. if search
// orders return the same result,its still not guaranteed its finding max-flow,that will
// require additional tests. if this test fails,however,we definitely kNow that the algo is not
// always finding max flow.
int last = -1;
for (int i = 0; i < 10; i++) {
Collections.shuffle(edgeList,random);
Graph<String,IntegerFlow> graph = new GraphBuilder().withEdges(edgeList).build();
int next = new FordFulkerson<>(graph,graph.get(0),graph.get(graph.vertexCount()-1)).maxflow();
if (last < 0) last = next;
Assertions.assertthat(next).isEqualTo(last);
}
}
@Property
void validMinCutCandidate (@ForAll @From("graphs") Graph<String,IntegerFlow> graph) {
// given the testing constraints we are not going to find the actual min-cut,as that would involve
// re-implementation in some form. however we can check if its possible that there is a valid min-cut
// very easily. if we find that its not even possible that a valid min-cut is specified by a solution
// we kNow that the algorithm can not be finding the true max-flow.
Vertex<String,IntegerFlow> source = graph.get(0);
Vertex<String,IntegerFlow> sink = graph.get(graph.vertexCount() - 1);
MaxIntegerFlow<String,IntegerFlow> algorithm = new FordFulkerson<>(graph,source,sink);
int flow = algorithm.maxflow();
int possibleCut = 0;
for (Vertex<String,IntegerFlow> vertex : graph.vertices()) {
if (vertex == sink) continue;
for (Traverser<Edge<String,IntegerFlow>> trav = vertex.outgoing(); trav.moveNext();) {
if (trav.get().label().available() == 0) {
possibleCut += trav.get().label().flow();
}
}
}
Assertions.assertthat(possibleCut).isGreaterThanorEqualTo(flow);
}
在这种情况下,我只是通过 id 指定源/目标顶点并添加一个流组件(可以是权重或任意数量的其他关联值)。该方案是从 [degree_min,degree_max] 中创建一个度数值列表,每个顶点一个,然后将该列表扩展为一个列表,其中每个源重复度数次。一旦我有了那个列表,我就可以生成目标和标签的序列并组合起来形成边缘。
这足以保证我有一个完整的顶点列表,并且每个顶点都有适当数量的输出边。但是我不认为这种方法可以很好地扩展以添加更现实/有用的约束。特别是考虑到可能需要额外的过滤和映射步骤,而且就目前情况而言,可能已经有太多...
例如,我认为能够对每个节点的边进行任意设置,然后加入任意设置以制作边的整体列表可能会有所帮助,但我在框架内看不到任何方法(例如组合面向组合从每个列表中获取的值,而不是连接列表)。
寻求任何改进建议。
解决方法
由于您的示例无法轻松重现(缺少某些依赖项),我试图通过阅读代码了解您正在创建什么样的图形。我可能错过了什么。
这是我想出的一个简单方法:
@Provide
Arbitrary<Set<Tuple2<String,Set<Tuple2<String,Integer>>>>> nodes() {
int maxVertices = 20;
int degreeMax = 4;
int minEdgeFlow = 1;
int maxEdgeFlow = 10;
Arbitrary<String> anyVertix = Arbitraries.strings().withCharRange('a','z').ofLength(3);
SetArbitrary<String> anyVertices = anyVertix.set().ofMinSize(1).ofMaxSize(maxVertices);
return anyVertices.flatMapEach((vertices,vertix) -> {
// Single vertix is a special case
if (vertices.size() <= 1) {
return Arbitraries.just(Tuple.of(vertix,Collections.emptySet()));
}
Set<String> possibleTargetVertices = new HashSet<>(vertices);
possibleTargetVertices.remove(vertix);
Arbitrary<Integer> anyEdgeFlow = Arbitraries.integers().between(minEdgeFlow,maxEdgeFlow);
Arbitrary<Tuple2<String,Integer>> anyConnection =
Combinators.combine(Arbitraries.of(possibleTargetVertices),anyEdgeFlow).as(Tuple::of);
SetArbitrary<Tuple2<String,Integer>> anyConnections = anyConnection.set().ofMaxSize(degreeMax);
return anyConnections.map(connections -> Tuple.of(vertix,connections));
});
}
@Property(tries = 100)
@Report(Reporting.GENERATED)
@StatisticsReport(label = "count nodes",format = NumberRangeHistogram.class)
@StatisticsReport(label = "max degree",format = Histogram.class)
void checkNodes(@ForAll("nodes") Set<Tuple2<String,Integer>>>> nodes) {
Statistics.label("count nodes").collect(nodes.size());
int maxDegree = nodes.stream().mapToInt(node -> node.get2().size()).max().orElse(0);
Statistics.label("max degree").collect(maxDegree);
}
此提供程序方法不会生成边列表,而是生成一组顶点及其连接和每个连接的边流。当然,一个可以转换成另一个。
我在生成器中努力的目标是最小化平面映射的数量,因为平面映射通常会使收缩变得更难。
也就是说,图形生成是一个您可以获得博士学位的主题,有些人也有。有几种标准方法可以生成图形(例如 https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_model)和许多更复杂的方法。您可能需要查看其他一些 SO 答案和资源:
- How to generate random graphs?
- How can I generate random graphs with test.check?
- https://blog.finxter.com/how-to-generate-random-graphs-with-python/
将这些方法翻译成 jqwik 代码有时很容易,有时则更复杂。
附言TypeUsage type,ArbitraryProvider.SubtypeProvider subtype
参数是可选的。仅添加您在方法中使用的那些。
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