In this paper, we define the reoptimization variant of the closest substring problem (CSP) under sequence addition. We show that, even with the additional information we have about the problem instance, the problem of finding a closest substring is still NP-hard. We investigate the combinatorial property of optimization problems called self-reducibility. We show that problems that are polynomia...

Four compact ROSAT X-ray sources very close to the nearby ultraluminous infrared galaxy Arp 220 (IC 4553) have been identified as medium-redshift QSOs. The closest pair lying symmetrically across the galaxy have almost identical redshifts z = 1.25, 1.26. All of the evidence suggests that these QSOs have been ejected from Arp 220 and have large intrinsic redshifts.

The problem of finding the least-squares solution to a system of linear equations where the unknown vector is comprised of integers, but the matrix coefficient and given vector are comprised of real numbers, arises in many applications: communications, cryptography, GPS, to name a few. The problem is equivalent to finding the closest lattice point to a given point and is known to be NP-hard. In...

We construct several new statistical zero-knowledge proofs with efficient provers, i.e. ones where the prover strategy runs in probabilistic polynomial time given an NP witness for the input string. Our first proof systems are for approximate versions of the Shortest Vector Problem (SVP) and Closest Vector Problem (CVP), where the witness is simply a short vector in the lattice or a lattice vec...

Divide and Conquer is a well known algorithmic procedure for solving many kinds of problem. In this procedure, the problem is partitioned into two parts until the problem is trivially solvable. Finding the distance of the closest pair is an interesting topic in computer science. With divide and conquer algorithm we can solve closest pair problem. Here also the problem is partitioned into two pa...

Given two datasets DA and DB the closest-pair query (CPQ) retrieves the pair (a,b), where a ∈ DA and b ∈ DB, having the smallest distance between all pairs of objects. An extension to this problem is to generate the k closest pairs of objects (k-CPQ). In several cases spatial constraints are applied, and object pairs that are retrieved must also satisfy these constraints. Although the applicati...

We present a simple greedy algorithm, QuickCP, for finding the closestpair of points on a plane. It is based on the observation that if two points are close to each other, then it is very likely that their sorted projections to x-axis and/or to y-axis will reflect that closeness. Therefore we order our search starting from the pairs with closest x-projections (and closest y-projections) to find...

An algorithm, described by Sedgewick, finds the distance between the closest pair of n given points in a plane using a variant of mergesort. This takes O(n logn) time. To prove this it is necessary to show that, in the merge phase of the algorithm, no more than a constant number of distances need to be checked for each point considered. Cormen, Leiserson and Rivest show that checking seven dist...

In many infeasible linear programs it is important to construct it to a feasible problem with a minimum pa-rameters changing corresponding to a given nonnegative vector. This paper defines a new inverse problem, called “inverse feasible problem”. For a given infeasible polyhedron and an n-vector a minimum perturba-tion on the parameters can be applied and then a feasible polyhedron is concluded.