Aditya Shastri

Metagraph-Based Substructure Pattern Mining

The need for mining structured data has increased in the past few years. One of the best studied data structures in computer science and discrete mathematics are graphs. Graph based data mining has become quite popular in the last few years. In this paper author presented Metagraph based data mining as a new approach in the field of traditional graph based mining. Metagraph is a new graph theoretic construct having set-to-set mapping in place of node to node as in conventional graph structure. We investigate new approaches for frequent Metagraph-based pattern mining in Metagraph datasets. We propose an algorithm for metagraph graph-based Substructure pattern mining which discovers frequent substructures without candidate generation. We apply a new lexicographic order for metagraphs, and map each sub metagraph to a unique minimum DFS code as its canonical label. Based on this lexicographic order. We develop an algorithm which adapts the depth-first search strategy to mine frequent connected submetagraph efficiently.

Supply chain management for two-level trade credit financing with selling price dependent demand under the effect of preservation technology

The present paper investigated the economic order quantity inventory model for a retailer under two-levels of trade credit to reflect the supply chain management (SCM). Here, it is assumed that the selling items are perishable such as fruits, fresh fishes, gasoline, photographic films, etc. It is assumed that potential worth of items can be increased by using preservation technology and the retailers trade credit period (M) offered by the supplier is longer than the customers trade credit period (N) offered by the retailer. It also assumed that the demand of the customer depends on the selling price of items. Theorems are developed to determine retailers optimal ordering policies and numerical examples are given to illustrate these theorems. It also observed that Goyal (1985), Shah (1993), Chung (1998) and Huang (2003) are the particular case of our proposed model. In addition, some managerial insights from the numerical examples are also concluded.

Edge-Bandwidth of Graphs

The edge-bandwidth of a graph is the minimum, over all labelings of the edges with distinct integers, of the maximum difference between labels of two incident edges. We prove that edge-bandwidth is at least as large as bandwidth for every graph, with equality for certain caterpillars. We obtain sharp or nearly sharp bounds on the change in edge-bandwidth under addition, subdivision, or contraction of edges. We compute edge-bandwidth for Kn, Kn,n, caterpillars, and some theta graphs.

Time-relaxed broadcasting in communication networks

Abstract Broadcasting is the process of information dissemination in communication networks (modelled as graphs) whereby a message originating at one vertex becomes known to all members under the constraint that each call requires one unit of time and at every step any member can call at most one of its neighbours. A broadcast graph on n vertices is a network in which message can be broadcast in the minimum possible (=⌊log2n⌋) time regardless of the originator. Broadcast graphs having the smallest number of edges are called minimum broadcast graphs, and are subjects of intensive study. On the other hand, in Shastri (1995) we have considered how quickly broadcasting can be done in trees. In this paper, we study how the number of edges in a minimum broadcast graphs decrease, as we allow addition time over ⌊log2 n⌋, until we get a tree. In particular, the sparsest possible time-relaxed broadcast graphs are constructed for small n(⩽15) and very sparse time-relaxed broadcast graphs are given for larger n(⩽65). General constructions are also provided putting bounds which hold for all n. Some of these constructions make use of the techniques developed in Bermond et al. (1995, 1992) and Chau and Liestman (1985).

Metagraph: A New Model of Data Structure

Often a carefully chosen data structure will allow the most efficient algorithm to be used. A well-designed data structure allows us to apply variety of critical operations by the few resources, both execution time and memory space. In this paper I introduce the concept of metagraph as a new model of data structure. Metagraph is graphical hierarchical data structure in which every node is a set having one or more elements. It has all the properties of graphs. In a metagraph, there is set to set mapping in place of node to node as in a conventional graph structure. In a metagraph as data structures data will be stored inside the computer memory either in the form of adjacency matrix or in adjacency list so that it can be used efficiently.

Broadcasting in General Networks I: Trees

Broadcasting is the process of information dissemination in communication networks whereby a message originated at one vertex becomes known to all members given that at each unit of time a vertex can pass the message to at most one of its neighbours. In this paper we consider the problem of broadcasting in trees which is a step towards studying broadcasting in general graphs, as oppose to the much studied problem of constructing broadcast graphs having the smallest number of edges in which message can be broadcast in minimum possible (= [log2n]) steps regardless of originator. Trees with the smallest possible broadcast time are exhibited for all n≤326, and for n sufficiently large existence of trees with broadcast time roughly 3/2 log2n is shown. It is also shown that broadcast time of a general tree can be computed in O(n) time.

An Evaluation of the CK Suite of Object-Oriented Software Metrics

Present study has been done to explore a set of metrics that can be used to build higher quality software. This needs software process improvement which requires measuring both the process and its performance. Managers working in the software development are giving more stress on process management. The focus to improve process and performance has increased the demand for software measures or metrics. Object-oriented development requires not only a different approach to design and implementation but it also requires different approach to software metrics. The approach to software metrics for object oriented programs must be different from the standard metrics set. Metrics such as line of code and cyclomatic complexity have become accepted standard for procedural programs but for object-oriented, there are many proposed object oriented metrics in the literature among which CK metrics (Chidamber and Kemerer) are the most popular and economic variable for commercial use. The result proposes a set of metrics that measures the conformance of a design to the desirable pattern.

Integrated defective production model for impatient customers with price dependent demand under the effect of learning

In this paper, a three-echelon supply chain model has been explored, comprising of a supplier, a producer and a retailer where demand rate is functionally related to the selling price. In this study, it is assumed that customers are impatient in nature so shortages occur at the end of retailer. Production process assumes to be imperfect and defective items reworked and available for sale as good ones. Number of defective items present in supplier end follows the learning curve. The model has been explored numerically as well, an optimal solution has been obtained and the sensitivity of that solution has also been checked with respect to various system parameters. The final outcome shows that the model is not only stable but also economically feasible.

Some sparse time-relaxed broadcast communication networks

Broadcasting is the process of information dissemination in communication networks (modelled as graphs) whereby a message originated at one vertex becomes known to all members under the constraints that each call requires one unit of time and at every step any member can call at most one of its neighbours. A broadcast graph on n vertices is a network in which message can be broadcast in minimum possible (=[log/sub 2/n]) time regardless of originator. Broadcast graphs having the smallest number of edges are called Minimum Broadcast Graphs, and are subject of intensive study. On the other hand, in Shastri (1995) we have considered how quickly broadcasting can be done in trees. In this paper, we construct more and more sparse time-relaxed broadcast graphs for some small values of n, as we allow additional time over [log/sub 2/n], until we get a tree.