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In this paper, we define and study error locating arrays (ELAs), which can be used in software testing for locating faulty interactions among parameters or components in a system. We give constructions of ELAs for arbitrary strength t, based on covering arrays. We show that the number of tests given by ELAs grows as O(log k), where k is the number of parameters/components in the system, assuming other quantities (the number g of values per parameter, the strength t of faulty interactions, and the number d of faulty interactions) are bounded by a constant. We then give a series of results for the case of pairwise interactions (t = 2). We study the computational complexity of deciding whether a graph describing the faulty pairwise interactions is "locatable." We characterize the locatable graphs for the binary case (g = 2). We design and analyze efficient algorithms that locate errors under certain assumptions on the structure of the faulty pairwise interactions. Under the assumption of known "safe values," our algorithm performs a number of tests that is polynomial in log k and d, where k is the number of parameters in the system and d is an upper bound on the number of faulty pairwise interactions. For the binary alphabet case, we provide an algorithm that does not require safe values and runs in expected polynomial time in log k whenever d ∈ O(log log k). [ABSTRACT FROM AUTHOR]

For several graph-theoretic parameters such as vertex cover and dominating set, it is known that if their sizes are bounded by k, then the treewidth of the graph is bounded by some function of k. This fact is used as the main tool for the design of several fixed-parameter algorithms on minor-closed graph classes such as planar graphs, single-crossing-minor-free graphs, and graphs of bounded genus. In this paper we examine whether similar bounds can be obtained for larger minor-closed graph classes and for general families of graph parameters, including all those for which such behavior has been reported so far. Given a graph parameter P, we say that a graph family F has the parameter-treewidth property for P if there is an increasing function t such that every graph G ∈ F has treewidth at most t(P(C)). We prove as our main result that, for a large family of graph parameters called contraction-bidimensional, a minor-closed graph family F has the parameter-treewidth property if F has bounded local treewidth. We also show "if and only if" for some graph parameters, and thus, this result is in some sense tight. In addition we show that, for a slightly smaller family of graph parameters called minor-bidimensional, all minor-closed graph families F, excluding some fixed graphs, have the parameter-treewidth property. The contraction-bidimensional parameters include many domination and covering graph parameters such as vertex cover, feedback vertex set, dominating set, edge-dominating set, and q-dominating set (for fixed q). We use our theorems to develop new fixed-parameter algorithms in these contexts. [ABSTRACT FROM AUTHOR]

Recently, D. Corneil found a simple 3-sweep lexicographic breadth first search (LexBFS) algorithm for the recognition of proper interval graphs. We point out how to modify Corneil's algorithm to make it a certifying algorithm, and then describe a similar certifying 3-sweep LexBFS algorithm for the recognition of proper interval bigraphs. It follows from an earlier paper that the class of proper interval bigraphs is equal to the better known class of bipartite permutation graphs, and so we have a certifying algorithm for that class as well. All our algorithms run in time O(m+n), including the certification phase. The certificates of representability (the intervals) can be authenticated in time O(m + n). The certificates of nonrepresentability (the forbidden subgraphs) can be authenticated in time O(n). [ABSTRACT FROM AUTHOR]

In this paper we examine problems motivated by on-line financial problems and stochastic games. In particular, we consider a sequence of entirely arbitrary distinct values arriving in random order, and must devise strategies for selecting low values followed by high values in such a way as to maximize the expected gain in rank from low values to high values. First, we consider a scenario in which only one low value and one high value may be selected. We give an optimal on-line algorithm for this scenario, and analyze it to show that, surprisingly, the expected gain is n - O(1), and so differs from the best possible off-line gain by only a constant additive term (which is, in fact, fairly small—at most 15). In a second scenario, we allow multiple nonoverlapping low/high selections, where the total gain for our algorithm is the sum of the individual pair gains. We also give an optimal on-line algorithm for this problem, where the expected gain is n²/8 - Θ(n log n). An analysis shows that the optimal expected off-line gain is n²/6 + Θ(1), so the performance of our on-line algorithm is within a factor of 3/4 of the best off-line strategy. [ABSTRACT FROM AUTHOR]