Adding Isolated Vertices Makes some Online Algorithms Optimal

An unexpected difference between online and offline algorithms is observed. The natural greedy algorithms are shown to be worst case online optimal for Online Independent Set and Online Vertex Cover on graphs with 'enough' isolated vertices, Freckle Graphs. For Online Dominating Set, the greedy algorithm is shown to be worst case online optimal on graphs with at least one isolated vertex. These algorithms are not online optimal in general. The online optimality results for these greedy algorithms imply optimality according to various worst case performance measures, such as the competitive ratio. It is also shown that, despite this worst case optimality, there are Freckle graphs where the greedy independent set algorithm is objectively less good than another algorithm. It is shown that it is NP-hard to determine any of the following for a given graph: the online independence number, the online vertex cover number, and the online domination number.Comment: A footnote in the .tex file didn't show up in the last version. This was fixe

Methods for evaluating Decision Problems with Limited Information

LImited Memory Influence Diagrams (LIMIDs) are general models of decision problems for representing limited memory policies (Lauritzen and Nilsson (2001)). The evaluation of LIMIDs can be done by Single Policy Updating that produces a local maximum strategy in which no single policy modification can increase the expected utility. This paper examines the quality of the obtained local maximum strategy and proposes three different methods for evaluating LIMIDs. The first algorithm, Temporal Policy Updating, resembles Single Policy Updating. The second algorithm, Greedy Search, successively updates the policy that gives the highest expected utility improvement. The final algorithm, Simulating Annealing, differs from the two preceeding by allowing the search to take some downhill steps to escape a local maximum. A careful comparison of the algorithms is provided both in terms of the quality of the obtained strategies, and in terms of implementation of the algorithms including some considerations of the computational complexity

Search algorithms for regression test case prioritization

Regression testing is an expensive, but important, process. Unfortunately, there may be insufficient resources to allow for the re-execution of all test cases during regression testing. In this situation, test case prioritisation techniques aim to improve the effectiveness of regression testing, by ordering the test cases so that the most beneficial are executed first. Previous work on regression test case prioritisation has focused on Greedy Algorithms. However, it is known that these algorithms may produce sub-optimal results, because they may construct results that denote only local minima within the search space. By contrast, meta-heuristic and evolutionary search algorithms aim to avoid such problems. This paper presents results from an empirical study of the application of several greedy, meta-heuristic and evolutionary search algorithms to six programs, ranging from 374 to 11,148 lines of code for 3 choices of fitness metric. The paper addresses the problems of choice of fitness metric, characterisation of landscape modality and determination of the most suitable search technique to apply. The empirical results replicate previous results concerning Greedy Algorithms. They shed light on the nature of the regression testing search space, indicating that it is multi-modal. The results also show that Genetic Algorithms perform well, although Greedy approaches are surprisingly effective, given the multi-modal nature of the landscape