The degree of dissimilarity between genome sequences of homologous species is a measure of the evolutionary distance between them. It serves as a metric in the construction of phylogenetic trees, which depict the evolutionary relationships and common ancestry among different species. Given two genome sequences, evolutionary distance is determined by estimating the number of global mutations that transform one sequence to the other. The computation of the evolutionary distance is done by modelling a genome with the corresponding permutation. Global rearrangement operations such as transposition that model a particular genomic mutation are studied by employing a combinatorial structure known as a cycle graph of the corresponding permutation. A cycle in a cycle graph that has odd length is called an odd cycle. In the context of the problem of sorting by transpositions (SBT), a valid 2-move is a transposition that increases the number of odd cycles in the cycle graph by two. A super oriented cycle (SOC) is an odd cycle C where C and one of the resultant cycles admit valid 2-moves. The minimum number of mutations required to transform a species S into a related species T is the distance from S to T under that mutation. Christie opined that characterizing SOCs will improve the lower bound of the transposition distance. We characterize super oriented cycles. Equivalent transformations on permutations like reduction and (g,b)-split preserve the transposition distance of a given permutation and map SBT to the corresponding SBT on a transformed simpler permutation. We introduce merge, a novel equivalent transformation. These results have applications in computing transposition and other distances between related species.

The optimization problem of covering a given geometrical region, such as a rectangle, with the minimum number of identical circles has been extensively studied in various disciplines. The paper introduces two quadratic time algorithms to solve two variants of the problem. The first algorithm computes the configurations or positions of the circles to cover the rectangle provided the circles cannot overlap. The second algorithm computes the same for the problem variant where the circles can overlap. The algorithms proved effective in handling diverse rectangle sizes and circle radii, efficiently solving the problem of covering a given rectangular region with the minimum number of identical circles and finding their positions. The empirical evaluation shows that the two algorithms compute the configuration of circles with minimum overlap or loss respectively.

Sorting permutations with various operations has applications in macro rearrangement of genes in a genome and the design of computer interconnection networks. Block-interchange is a powerful operation that swaps two substrings that are called as blocks in literature, in a given permutation. When the blocks are restricted to be adjacent then one obtains a well studied operation: transposition. We call either a prefix or a suffix as an extreme. Restricting one of the swapped blocks to be an extreme in block-interchange operation yields a prefix or a suffix block-interchange respectively, the two types of extreme block-interchanges. For prefix block-interchange operation over permutations we design: (i) an optimum algorithm to sort reverse permutation, Rn, in n/2 moves, (ii) a simple 2-approximation algorithm, and (iii) for permutations with O(1) cycles, a 4/3 approximation algorithm. Due to symmetry, these results apply to suffix block-interchange operation also.

Sorting permutations by transposition are a well-studied combinatorial optimization problem having applications in comparative genomics. The problem belongs to the NP-hard class, and several approximation algorithms are existent. Altinier, Oliveira and Dias proposed a machine learning approach for sorting permutations by two types of rearrangement operations, namely reversals and block transpositions. This paper discusses an application of their approach for sorting permutations by using a single operation, namely transposition under an improved setting. It also discusses the application of the method on permutations from toric equivalence classes and shows that comparable results with lesser computation overhead can be obtained.

Peer to peer is an overlay network of interconnected nodes with high scalability, reliability, efficiency, and low setup cost. A fundamental problem in p2p networks is resource discovery. Several graph-based resource discovery algorithms in unstructured p2p networks are existent. The performance analysis of these algorithms were conducted under constrained settings like fixed hop count, fixed maximum number of neighbours, etc. In this work, we revisit these algorithms on random networks. Such analysis can give better insights and hence more realistic results, because real-world networks are often random.

E-commerce platform has brought about a revolutionary change in the way people conduct shopping. In India, the number of digital buyers in 2016 was 130.4 million and by 2021 the number is estimated to increase to around 400 million. In this paper we propose a Levenshtein distance based sentiment classification engine that reads the reviews across different websites for a given product, eventually providing a metric that would help the user in making an informed choice of product.

Data transfer amongst peers in a network without a central authority to regulate traffic, is on the ascendancy in the recent years. In this paper, we propose a k-clique based overlay network formation using multi key-single value pair mapping mechanism within a peer to peer network. This clique based model aims to discover resources of the same metadata type within a cluster of subnet with a minimum of hops as possible subject to the nodes having certain properties. The discovery of a subset of resources sharing similar characteristics is essential in the context of requirements being dynamic, in fields related to Internet of Things and Cloud systems. The simulated experiment validates our approach as it discovers resources in very less number of hops.

A Multiplicative Spanner is a spanning sub-graph H(V, E ' ) of a graph G(V, E) such that where distance(u, v, G) is the shortest distance between the vertices u and v in G. The parameter t is called the multiplicative stretch of the spanner. When the size of the graph is reduced to construct a spanner, the shortest distance between the vertices increases, consequently the stretch factor also increases. It is known that the construction of spanners with optimum size-stretch is hard. Many researchers proposed efficient algorithms that yield proven near optimal results. In this paper we propose a quadratic time algorithm to construct multiplicative t-spanners with a bound on the stretch factor.

The notion of a multiplicative t - spanner was defined by David Peleg and Alejandro Scha̅fer in 1989. A vertexspanning sub graph S, of a simple graph H(V, E) in which the pairwise distance between any two vertices is less than or equal to t times that in H is called a puerly multiplicative t - spanner. The real valued parameter t (> 1) denotes the maximum possible multiplicative stretch of u-v distances in the spanner S. Although the combinatorial construction of a t-spanner with m or fewer edges for a given m and t (MTS problem henceforth) is known to be difficult, it is possible to construct MTS efficiently for graphs which satisfies certain properties. In this paper we characterize an infinite family of graph for which the MTS problem can be solved efficiently. Based on the characterization we posit a (n) algorithm for constructing an MTS.

Given a set P of n points in R^d, a tour is a closed simple path that covers all the given points, i.e. a Hamiltonian cycle. points are collinear then the points are said to be in general position. A link is a line segment connecting two points and a rectilinear link is parallel to one of the axes. The problems of defining a path and a tour with minimum number of links, also known as Minimum-Link Covering Path and Minimum-Link Covering Tour respectively are proven to be NP-hard in R^2. The corresponding rectilinear versions are also NP-hard in R^2. A set of points is said to be in general position for rectilinear versions of the problems if no two points share any coordinate. We call a set of points in R^d to be in relaxed general position if no three points share any coordinate and any two points can share at most one coordinate. That is, if the points are either in general position or in relaxed general position then an axis parallel line can contain at most one point. If points are in relaxed general position then these problems are NP-hard in R^10. We prove that these two problems are in fact NP-hard in R^4. If points in R^d, d>1 are in general position then the time complexities of these problems, both basic and rectilinear versions, are unknown.