Abstract. We investigate the power of a family of greedy algorithms for the independent set problem graphs of maximum degree three. These algorithm iteratively select vertices of minimum degree, but differ in the secondary rule for choosing among many candidates. We present two such algorithms that run in linear time, and show their performance ratios to be 3/2 and 9/7 ~ 1.28, respectively. This also translates to good ratios for other classes of low-degree graphs. We also show certain inherent limitations in the power of this family of algorithm: any algorithm that greedily selects vertices of minimum degree has a performance ratio at least 1.25 on degree-three graphs, even if given an oracle to choose among candidate vertices of minimum degree. IntroductionAn independent set of a graph G is a subset of vertices in which no two are adjacent. The MAX INDEPENDENT SET problem is that of finding an independent set of maximum cardinality. It is one of the core A/P-hard problems [4], and thus, polynomial time exact algorithms are unlikely to exist. It is therefore interesting to explore algorithms that produce solutions that are not always optimal but are close to optimal. The quality of an approximation algorithm is generally measured by the performance ratio, or the maximum ratio of the size of an optimal solution (the size of the maximum independent set) to the size of the solution found by the algorithm. In this paper we focus on a central case of bounded-degree graphs, namely when the maxinmm degree is at most three. Since the independent set problem is polynomial solvable when maximum degree is two, this problem can be thought of as the initial frontier of A/P-hardness of the problem. Also, many of the results for higher degrees use reductions to lower degree cases, in which the degree-three plays the role of the basis case [3,7,5,2], and improvements for that case translate to improvements for all odd degrees.Let us review the known results about approximating independent sets in degree-three graphs. Hochbaum [9] presented an algorithm with a 1.5 ratio, that runs in time proportional to bipartite matching or O(nl5

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Multi hop wireless ad hoc networks can be formed by a group of wireless nodes without requiring the use of a preexisting infastructure. However such an ad hoc network environment is hard to administer, so applications cannot assume they know which services are exist and where they are hosted. A service discovery that provides automatic discovery of desired services to the applications i s particularly important to save the userfom the trouble of the con$guring task and takes advantage of the full range ofprovided services.In this paper, we propose a new service discovery method for multi hop wireless ad hoc networks. The method provides an efficient method of service discovery for increasing the number of discoverable services. We evaluate the proposed method through a simulation study and compare it with the existing method. Results show that the proposed method achieves better performance in terms of the number of discoverable services, while the number of control messages and response time for discovering the services are almost the same as the existing method.