External watchman routes

We consider the problem of finding a shortest watchman route from which the exterior of a polygon is visible (external watchman route). We present an O (n ⁴ log logn) algorithm to find shortest external watchman routes for simple polygons by transforming the external watchman route problem to a set of internal watchman route problems. Also, we present faster external watchman route algorithms for special cases. These include optimal O (n) algorithms for convex, monotone, star and spiral polygons and an O (n log logn) algorithm for rectilinear polygons.This work was supported in part by a grant from Texas Instruments, Inc. to S. Ntafos     

An Evaluation of Random Testing

Random testing of programs has usually (but not always) been viewed as a worst case of program testing. Testing strategies that take into account the program structure are generally preferred. Path testing is an often proposed ideal for structural testing. Path testing is treated here as an instance of partition testing, where by partition testing is meant any testing scheme which forces execution of at least one test case from each subset of a partition of the input domain. Simulation results are presented which suggest that random testing may often be more cost effective than partition testing schemes. Also, results of actual random testing experiments are presented which confirm the viability of random testing as a useful validation tool.     

On some reliability estimation problems in random and partitiontesting

Studies have shown that random testing can be an effective testing strategy. One of the goals of testing is to estimate the reliability of the program from the test outcomes. The authors extend the Thayer-Lipow-Nelson reliability model (R. Thayer et al., 1978) to account for the cost of errors. They also compare random testing with partition testing by examining upper confidence bounds for the cost weighted performance of the two strategies     

On comparisons of random, partition, and proportional partitiontesting

Early studies of random versus partition testing used the probability of detecting at least one failure as a measure of test effectiveness and indicated that partition testing is not significantly more effective than random testing. More recent studies have focused on proportional partition testing because a proportional allocation of the test cases (according to the probabilities of the subdomains) can guarantee that partition testing will perform at least as well as random testing. We show that this goal for partition testing is not a worthwhile one. Guaranteeing that partition testing has at least as high a probability of detecting a failure comes at the expense of decreasing its relative advantage over random testing. We then discuss other problems with previous studies and show that failure to include important factors (cost, relative effectiveness) can lead to misleading results     

On partitioning rectilinear polygons into star-shaped polygons

We present an algorithm for finding optimum partitions of simple monotone rectilinear polygons into star-shaped polygons. The algorithm may introduce Steiner points and its time complexity isO(n), wheren is the number of vertices in the polygon. We then use this algorithm to obtain anO(n logn) approximation algorithm for partitioning simple rectilinear polygons into star-shaped polygons with the size of the partition being at most six times the optimum.     

On partitioning rectilinear polygons into star-shaped polygons

We present an algorithm for finding optimum partitions of simple monotone rectilinear polygons into star-shaped polygons. The algorithm may introduce Steiner points and its time complexity isO(n), wheren is the number of vertices in the polygon. We then use this algorithm to obtain anO(n logn) approximation algorithm for partitioning simple rectilinear polygons into star-shaped polygons with the size of the partition being at most six times the optimum.     

A comparison of some structural testing strategies

Several structural testing strategies are compared in terms of their relative coverage of the program's structure and also in terms of the number of test cases needed to satisfy each strategy. Some of the deficiencies of such comparisons are discussed     

On legal path problems in digraphs

In this paper we consider the problem of finding a legal source to sink (s-t) path in a digraph G = (V, E), for which a set of impossible paths is specified. This problem arises in program testing. An efficient algorithm is presented for the case when G is an acyclic digraph and the general problem is shown to be computationally intractable.     

On Required Element Testing

In this paper we introduce two classes of program testing strategies that consist of specifying a set of required elements for the program and then covering those elements with appropriate test inputs. In general, a required element has a structural and a functional component and is covered by a test case if the test case causes the features specified in the structural component to be executed under the conditions specified in the functional component. Data flow analysis is used to specify the structural component and data flow interactions are used as a basis for developing the functional component. The strategies are illustrated with examples and some experimental evaluations of their effectiveness are presented.     

Guarding a Terrain by Two Watchtowers

Given a polyhedral terrain T with n vertices, the two-watchtower problem for T asks to find two vertical segments, called watchtowers, of smallest common height, whose bottom endpoints (bases) lie on T, and whose top endpoints guard T, in the sense that each point on T is visible from at least one of them. There are three versions of the problem, discrete, semi-continuous, and continuous, depending on whether two, one, or none of the two bases are restricted to be among the vertices of T, respectively.