We consider binary search trees, where rebalancing transformations need not be connected with updates but may be delayed. For standard AVL tree rebalancing, we prove that even though the rebalancing operations are un-coupled from updates, their total number is bounded by O(M log(M +N)), where M is the number of updates to an AVL tree of initial size N. Hence, relaxed balancing of AVL trees come...

RIFO, as has been proposed by Nebel et al. (Nebel, Dimopoulos, and Koehler 1997), is a method that can automatically detect irrelevant information in planning tasks. The idea is to remove such irrelevant information as a pre-process to planning. While RIFO has been shown to be useful in a number of domains, its main disadvantage is that it is not completeness preserving. Furthermore, the pre-pr...

Given a set of users U , a set of facilities F , and a query facility q, a reverse nearest neighbors (RNN) query retrieves every user u for which q is its closest facility. Since q is the closest facility of u, the user u is said to be influenced by q. In this paper, we propose a relaxed definition of influence where a user u is said to be influenced by not only its closest facility but also ev...

We analyze the complexity of verifying whether a given element is close to a solution element. Closeness is measured by two nonnegative parameters, " and. If = 0, then we get the strong veriication problem which usually cannot be solved in the worst case setting, see Wo zniakowski 90]. For > 0, we have the relaxed veriication problem which is studied in this paper in the worst case setting. We ...

In Description Logics (DL) knowledge bases (KBs), information is typically captured by clear-cut concepts. For many practical applications querying the KB by crisp concepts is too restrictive; a user might be willing to lose some precision in the query, in exchange of a larger selection of answers. Similarity measures can offer a controlled way of gradually relaxing a query concept within a use...

The magnetization of a ferromagnetic sample solves a non-convex variational problem, where its relaxation by convexifying the energy density resolves relevant macroscopic information. The numerical analysis of the relaxed model has to deal with a constrained convex but degenerated, nonlocal energy functional in mixed formulation for magnetic potential u and magnetization m. In [C. Carstensen an...

The hm admissible heuristics for (sequential and temporal) regression planning are defined by a parameterized relaxation of the optimal cost function in the regression search space, where the parameter m offers a trade-off between the accuracy and computational cost of the heuristic. Existing methods for computing the hm heuristic require time exponential in m, limiting them to small values (m ...