The exact string matching problem is to find the occurrences of a pattern of length m from a text of length n symbols. We develop a novel and unorthodox filtering technique for this problem. Our method is based on transforming the problem into multiple matching of carefully chosen pattern subsequences. While this is seemingly more difficult than the original problem, we show that the idea leads...

Along the way, by way of illustration, I evaluate various players and teams with respect to baseadvance average. The evaluation of teams leads to further statistical comparisons. Here, the results are equally decisive in favor of base-advance average. For example, over the period 2000-2004, baseadvance average for-and-against predicts wins just as well as runs for-and-against. This is because, ...

One important reason to consider average case complexity is whether all or at least some signi cant part of NP can be solved e ciently on average for all reasonable distributions Let PP comp be the class of problems which are solvable in average polynomial time for every polynomial time computable input distribution Following the framework of Levin the above question can now be formulated as Is...

A number of objective functions in clustering problems can be described with submodular functions. In this paper, we introduce the minimum average cost criterion, and show that the theory of intersecting submodular functions can be used for clustering with submodular objective functions. The proposed algorithm does not require the number of clusters in advance, and it will be determined by the ...

We are interested in average changes in outcome y after a policy change. As in the case of the medical field, we are interested in the outcomes of a new medicine, including its effectiveness and its side effect. To do that, it is typical that we randomly divide patients into two groups, the treatment group, and the control group. The treatment group is given the medicine while the control group...

Let I = [0, N − 1] denote the set of indices. We define the set of states S to contain all maps of type I → R for fixed positive N ∈ N (representing the number of agents). For each s ∈ S, i ∈ I, s(i) represents the value held by the agent with ID i. We denote the arbitrarily fixed start state s0. We introduce the function g whose domain MR is the set of non-empty finite multisets of real number...