On the Independent Set and Common Subgraph Problems in Random Graphs
نویسنده
چکیده
In this paper, we develop efficient exact and approximate algorithms for computing a maximum independent set in random graphs. In a random graph G, each pair of vertices are joined by an edge with a probability p, where p is a constant between 0 and 1. We show that, a maximum independent set in a random graph that contains n vertices can be computed in expected computation time 2 2 2 . Using techniques based on enumeration, we develop an algorithm that can find a largest common subgraph in two random graphs in n and m vertices (m ≤ n) in expected computation time 2 1 2 log 5 3 2 . In addition, we show that, with high probability, the parameterized independent set problem is fixed parameter tractable in random graphs and the maximum independent set in a random graph in n vertices can be approximated within a ratio of 2n 2 √ log2 n in expected polynomial time.
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عنوان ژورنال:
- CoRR
دوره abs/1308.1556 شماره
صفحات -
تاریخ انتشار 2013