Joydeb Ghosh

Bio: Joydeb Ghosh is an academic researcher from University of North Bengal. The author has contributed to research in topics: Coin problem & Group testing. The author has an hindex of 2, co-authored 6 publications receiving 12 citations.

A New Algorithm to Represent a Given k-ary Tree into Its Equivalent Binary Tree Structure

Abstract: In this paper we have developed an algorithm that converts a given k-ary tree, for any k ≥ 3, to its equivalent binary tree structure. The binary tree is generated in O(n) time, for a k-ary tree with a total of n nodes. The algorithm is designed aiming at reducing the height of the constructed binary tree. The constructed tree does not contain any free links in the non-leaf nodes. That means the constructed tree is like a complete binary tree, where only leaves have no children, and nodes other than leaf nodes contain child (children) and some other valid information of the given k-ary tree.

A generalized algorithm for solving n coins problem

Abstract: Eight coins problem is a well-known problem in mathematics as well as in computer science. In this problem eight coins are given, say A, B, C, D, E, F, G, and H, and we are told that only one is counterfeit (or false), as it has a different weight than each of the others. We want to determine which coin it is, making use of an equal arm balance. At the same time we want to identify the counterfeit coin using a minimum number of comparisons and determine whether the false coin is heavier or lighter than each of the remaining. In this paper, we develop algorithms for solving the counterfeit coin problem for any given number n of coins. The first algorithm is in essence based on the existing classical solution for the eight coins problem (with slight modification) for larger values of n, where n is a power of two beyond eight, as two and four being base cases. Then we develop an algorithm for solving n coins problem, where n is even but not power of two, i.e., the numbers are six, ten, 12, 14, 18, 20, etc. At the end, we have extended the same to solve the counterfeit coin problem for odd number of coins as well.

An algorithm for identifying two unequal heavier / lighter coins out of n given coins

Abstract: Counterfeit coin problem has been considered for a very long time and is a topic of great significance in Mathematics as well as in Computer Science. In this problem, out of« given coins, two or more false coins (the coins are classified as false because their weights are different when compared to a standard coin) are present which have the same appearance as the other coins. This problem belongs to the class of combinatorial group testing problem which finds several applications in hidden graph construction problem etc. In this paper, we have constructed an optimal algorithm to determine two false coins out of a given number of coins. In addition, our objective is to solve the problem in minimum number of comparisons with the help of an equal arm balance. Our proposed algorithm is able to find out the fake coins using O(log n) comparisons.

An endeavour to find two unequal false coins

Abstract: The counterfeit coin problem is well-known and truly interesting in Computer Science, Game theory, and also in Mathematics In this problem the objective is to detect the fake coin(s) of identical appearance but different weight in minimum number of comparisons The word counterfeit most frequently describes forgeries of currency or documents, but can also describe software, pharmaceuticals, clothing, and more recently, motorcycles and cars, especially when these result in patent or trademark infringement Finding one fake coin among n coins is tricky enough and complex The problem becomes rigorous when there are two fake coins, as the false coin pair may form several different combinations that make the problem particularly tricky and complex to solve In this paper we have developed a new algorithm for solving two versions of the two counterfeit coins problem in O(log n) time, where n is the number of coins given

The first algorithm for solving two coins counterfeiting with ω(ΔH) = ω(ΔL)

Abstract: Counterfeit coin problem is of utmost importance and it is truly interesting in Computer Science and Game theory as well as in Mathematics In this problem the objective is to detect the fake coin(s) of identical appearance but of different weight in minimum number of comparisons The word counterfeit is most frequently applicable to forgeries of currency or documents, but can also describe software, pharmaceuticals, clothing, and more recently, motorcycles and other vehicles, especially when these result in patent or trademark infringement In this paper we have developed a new algorithm for solving two counterfeit coins problem in linear time, where n is the total number of coins given However, this is the first algorithm that identifies and solves the problem, given the false coins with type ω(ΔH) = ω(ΔL), ie, one false coin is heavier and another is lighter than a true coin, and their difference in weight from the true coin is equal However, this is the degenerate case in the field of two counterfeit coins problem

Graph theory with applications to engineering and computer science, by Narsingh Deo. Pp xvii, 478. 1974. SBN 0 13 363473 6 (Prentice-Hall)

Abstract: Graph Theory with Applications to Engineering and Computer ... This outstanding introductory treatment of graph theory and its applications has had a long life in the instruction of advanced undergraduates and graduate students in all areas that require knowledge of this subject. The first nine chapters constitute an excellent overall introduction, requiring only some knowledge of set theory and matrix algebra.

Using branching-property preserving Prüfer Code to encode solutions for particle swarm optimisation

Abstract: In the area of applied optimisation, heuristics are a popular means to address computational problems of high complexity Modelling the problem and mapping all variations of its solution into a so-called solution space are integral parts of this process Representing solutions as graphs is common and, for a special type of graph, Prufer Code (PC) offers a computationally efficient mapping (algorithms of Θ(n)-complexity are known) to n—2 dimensional Euclidean space However, this encoding does not preserve properties such as eg locality and therefore PC has been shown to be a bad choice for entire classes of problems We argue that PC does allow the preservation of some properties (eg degree of branching and branching vertices) and that these are sufficiently relevant for certain types of problems to motivate encoding them in PC We present our investigations and provide an example where PC has been shown to be a useful encoding

K-ary tree to binary tree conversion through complete height balanced technique

Abstract: Technologies are generally provided for converting a k-ary tree to an equivalent height balanced binary tree. A k-ary tree root may be first set as the binary tree root. Nodes may then be inserted in the binary tree based on nodes of the k-ary tree. First two children of each k-ary tree node may be inserted as left and right children in the binary tree. If there are additional children, those may be inserted into a child queue. If there are less than two children in the k-ary tree, children from the child queue may be used to fill the left and right child nodes in the equivalent binary tree repeating the process level-wise until all nodes in the k-ary tree are processed.

Cluster Based Architecture and Algorithm to Improve the Design of Social Networks

Abstract: In a social network people are connected by relationships, business purpose or transaction activity. The increasing demand of social network analysis and how to improve the architecture is of utmos...

An algorithm for identifying two unequal heavier / lighter coins out of n given coins

Abstract: Counterfeit coin problem has been considered for a very long time and is a topic of great significance in Mathematics as well as in Computer Science. In this problem, out of« given coins, two or more false coins (the coins are classified as false because their weights are different when compared to a standard coin) are present which have the same appearance as the other coins. This problem belongs to the class of combinatorial group testing problem which finds several applications in hidden graph construction problem etc. In this paper, we have constructed an optimal algorithm to determine two false coins out of a given number of coins. In addition, our objective is to solve the problem in minimum number of comparisons with the help of an equal arm balance. Our proposed algorithm is able to find out the fake coins using O(log n) comparisons.