Small Longest Tandem Scattered Subsequences

We consider the problem of identifying tandem scattered subsequences within a string. Our algorithm identifies a longest subsequence which occurs twice without overlap in a string. This algorithm is based on the Hunt-Szymanski algorithm, therefore its performance improves if the string is not self similar, which occurs naturally on strings over large alphabets. Our algorithm relies on new results for data structures that support dynamic longest increasing sub-sequences. In the process we also obtain improved algorithms for the decremental string comparison problem.

Fault Localizations Through Feature Selections

We introduce a novel application of feature ranking methods to the fault localization problem. We envision the problem of localizing causes of failures as instances of ranking program’s elements where elements are conceptualized as features. In this paper, we define features as program’s statements. However, in its fine-grained definition, the idea of program’s features can refer to any traits of programs. This paper proposes feature ranking-based algorithms. The algorithms analyze execution traces of both passing and failing test cases, and extract the bug signatures from the failing test cases. The proposed procedure extracts possible combinations of program’s elements when executed together from bug signatures. The feature ranking-based algorithms then order statements according to the suspiciousness of the combinations. When viewed as sequences, the combination of program’s elements produced and traced in bug signatures can be utilized to reason about the common longest subsequence. The common longest subsequence of bug signatures represents the common statements executed by all failing test cases and thus provides a means for identifying statements that contain possible faults. Our evaluation indicates that the proposed feature-based fault localization outperforms existing fault localization ranking schemes.

Permutation Pattern matching in (213, 231)-avoiding permutations

Given permutations σ of size k and π of size n with k < n, the permutation pattern matching problem is to decide whether σ occurs in π as an order-isomorphic subsequence. We give a linear-time algorithm in case both π and σ avoid the two size-3 permutations 213 and 231. For the special case where only σ avoids 213 and 231, we present a O(max(kn 2 , n 2 log log n)-time algorithm. We extend our research to bivincular patterns that avoid 213 and 231 and present a O(kn 4)-time algorithm. Finally we look at the related problem of the longest subsequence which avoids 213 and 231.