This paper presents a new in-place pseudo linear radix sorting algorithm. The proposed algorithm, called MSL (Map Shuffle Loop) is an improvement over ARL (Maus, 2002). The ARL algorithm uses an in-place permutation loop of linear complexity in terms of input size. MSL uses a faster permutation loop searching for the next element to permute group by group, instead of element by element. The alg...

Let Q(A) be number of comparisons done on input array A: (A) For 1 ≤ i < j < n let R ij be the event that rank i element is compared with rank j element. (B) X ij is the indicator random variable for R ij. That is, X ij = 1 if rank i is compared with rank j element, otherwise 0. Q(A) = ∑ 1≤i<j≤n X ij and hence by linearity of expectation,

Let Q(A) be number of comparisons done on input array A: (A) For 1 ≤ i < j < n let R ij be the event that rank i element is compared with rank j element. (B) X ij is the indicator random variable for R ij. That is, X ij = 1 if rank i is compared with rank j element, otherwise 0. Q(A) = ∑ 1≤i<j≤n X ij and hence by linearity of expectation,

We consider the join operation in metric spaces. Given two sets A and B of objects drawn from some universe U, we want to compute the set A  B = {(a, b) ∈ A × B | d(a, b) ≤ r} efficiently, where d : U×U → R is a metric distance function and r ∈ R is user supplied query radius. In particular we are interested in the case where we have no index available (nor we can afford to build it) for eithe...

We introduce a new online algorithm for the multiselection problem which performs a sequence of selection queries on a given unsorted array. We show that our online algorithm is 1-competitive in terms of data comparisons. In particular, we match the bounds (up to lower order terms) from the optimal offline algorithm proposed by Kaligosi et al.[ICALP 2005]. We provide experimental results compar...

The paper questions the robustness of average case time complexity of the fast and popular quicksort algorithm. Among the six standard probability distributions examined in the paper, only continuous uniform, exponential and standard normal are supporting it whereas the others are supporting the worst case complexity measure. To the question -why are we getting the worst case complexity measure...

The analyses of many algorithms and data structures (such as digital search trees) for searching and sorting are based on the representation of the keys involved as bit strings and so count the number of bit comparisons. On the other hand, the standard analyses of many other algorithms (such as Quicksort) are performed in terms of the number of key comparisons. We introduce the prospect of a fa...