Mohammad Kaykobad

Bangladesh University of Engineering and Technology | BUET · Department of Computer Science and Engineering

Updating and querying on a range is a classical algorithmic problem with a multitude of applications. The Segment Tree data structure is particularly notable in handling the range query and update operations. A Segment Tree divides the range into disjoint segments and merges them together to perform range queries and range updates elegantly. Althou...

Updating and querying on a range is a classical algorithmic problem with a multitude of applications. The Segment Tree data structure is particularly notable in handling the range query and update operations. A Segment Segment Tree divides the range into disjoint segments and merges them together to perform range queries and range updates elegantly...

A DNA-binding protein (DNA-BP) is a protein that can bind and interact with a DNA. Identification of DNA-BPs using experimental methods is expensive as well as time consuming. As such, fast and accurate computational methods are sought for predicting whether a protein can bind with a DNA or not. In this paper, we focus on building a new computation...

In this paper, we propose techniques for dynamically adjusting heartbeat or keep-alive interval of long-lived TCP connections, particularly the ones that are used in push notification service in mobile platforms. When a device connects to a server using TCP, often times the connection is established through some sort of middle-box, such as NAT, pro...

Background Development of biologically relevant models from gene expression data notably, microarray data has become a topic of great interest in the field of bioinformatics and clinical genetics and oncology. Only a small number of gene expression data compared to the total number of genes explored possess a significant correlation with a certain...

This book constitutes the proceedings of the 10th International Workshop on Algorithms and Computation, WALCOM 2016, held in Kathmandu, Nepal, in March 2016. The 27 full papers presented together with 4 invited talks were carefully reviewed and selected from 68 submissions. The papers cover a wide range of topics such as approximation algorithms,...

Any tree with n vertices is conjectured to be graceful if its vertices can be labeled using integers 0, 1, · · · , n − 1 such that each vertex label as well as the corresponding edge label is distinct throughout the tree. There has been multiple attempts with different approaches to prove this conjecture but it remains the same. Here we will discus...

Classical Huffman codes have a very good compression performance over traditional systems. Yet, more efficient encoding is possible by considering and applying techniques that treat the binary bits differently considering requirement of storage space, energy consumption, speed of execution and so on. Future transmission systems are likely to be mor...

Graceful labeling is one of the most researched problems. One of the earliest results is that caterpillars are graceful. We show that caterpillars connected to a vertex recursively satisfying certain conditions are also graceful.

A tree is graceful if it has a graceful labeling. A graceful labeling of a tree T with m edges is a function f: V(T)→ {0,………,m} such that distinct vertices receive distinct numbers and {|f(u)-f(v)|: uv ϵ E(T)} ={1,……..,m}.The problem of whether or not all trees are graceful is still open. Many classes of trees have already been proved graceful such...

A Hamiltonian path in a graph is a path involving all the vertices of the graph. In this paper, we revisit the famous Hamiltonian path problem and present new sufficient conditions for the existence of a Hamiltonian path in a graph.

In this paper, we present Dirac-type sufficient conditions for a bipartite graph to possess a Hamiltonian path. We also define a seemingly new family of bipartite graphs, which we call the ZZ graphs. We show that our sufficient condition can also ensure Hamiltonicity unless the graph is a ZZ graph.

This chapter presents Bangla (widely known as Bengali) Automatic Speech Recognition (ASR) techniques by evaluating the different speech features, such as Mel Frequency Cepstral Coefficients (MFCCs), Local Features (LFs), phoneme probabilities extracted by time delay artificial neural networks of different architectures. Moreover, canonicalization o...

A Hamiltonian path in a graph is a path involving all the vertices of the graph. In this paper, we revisit the famous Hamiltonian path problem and present new sufficient conditions for the existence of a Hamiltonian path in a graph. 1. Introduction Hamiltonian paths and cycles are named after William Rowan Hamilton who invented the puzzle that inv...

In this paper, we present an interesting modification to the heap structure which yields a better comparison-based in-place heapsort algorithm. The number of comparisons is shown to be bounded by nlogn+nlog*n−0.546871n which is 0.853129n+nlog*n away from the optimal theoretical bound of nlogn−1.44n.

Given a set of n points in the plane, the problem of computing the circular ordering of the points about a viewpoint v and efficiently maintaining this ordering information as v moves is well defined in computer graphics and animation. Each of the unique circular ordering in respect to v is called as view. In this paper, our task is to generalize t...

In this paper we present some interesting results involving summation of series in particular trigonometric ones. We failed to locate these results in existing literature or in the web like MathWorld (http://mathworld.wolfram.com/) nor could we derive them using software for analytical computation like Maple. The identities are beautiful and involv...

In any language the letters of that language must be detected unambiguously to form words or sentences of that language. In this paper, a grammar is represented for the rules of conjugate and single letters in the alphabet of Bangla language and then an automaton is developed to represent the grammar. At first, rules of conjugate and single Bangla...

Divide and Conquer is a well known algorithmic procedure where the problem space to be solved is partitioned into two sub problems and each sub problem is considered as a separate problem and is partitioned again. This is done until the problem is trivially solvable. However, it is theoretically and practically observed that some times partitioning...

Since finding whether a graph has a Hamiltonian path or Hamiltonian cycle are both NP-complete problems, researchers have been formulating sufficient conditions that ensure the path or cycle. Rahman and Kaykobad (2005) [2] presented a sufficient condition for determining the existence of Hamiltonian path. Three recent works–Lenin Mehedy, Md. Kamrul...

The terrain generation approach proposed in dasiaParametrically controlled terrain generation, (Proceedings of GRAPHITE 2007)psila focuses on generation of terrains having mountains of prespecified heights and spreads of base regions and peaks nearly at prespecified locations. However, inability to produce mountain ranges is a shortcoming of the al...

Rahman and Kaykobad introduced a shortest distance based condition for finding the existence of Hamiltonian paths in graphs as follows: Let G be a connected graph with n vertices, and if d(u) + d(v) + delta(u, v) ges n + 1, for each pair of distinct non-adjacent vertices u and v in G, where delta(u, v) is the length of a shortest path between u and...

The problem of ranking players in a round-robin tournament, in which the outcome of any match is a win or a loss, is to rank them according to their performances in the tournament. In this paper we have improved the previously developed majority spanning tree (MST) algorithm for solving this problem, where the number of violations has been chosen a...

A Hamiltonian cycle is a closed path through all the vertices of a graph. Since discovering whether a graph has a Hamiltonian path or a Hamiltonian cycle are both NP-complete problems, researchers concentrated on formulating sufficient conditions that ensure Hamiltonicity of a graph. A recent paper (Rahman M. Sohel and Kaykobad M., "On Hamiltonian...

In this paper we present a new data structure for implementing heapsort algorithm for pairs of which can be simultaneously stored and processed in a single register. Since time complexity of Carlsson type variants of heapsort has already achieved a leading coefficient of 1, concretely nlg n + nlglg n, and lower bound theory asserts that no comparis...

DiskTrie is an efficient external-memory data structure for storing strings in mobile devices using flash memory. It supports Lookup and Prefix-Matching operations with a constant internal memory,and linear processing requirements. The number,of disk accesses it takes to search for a string among n unique finite strings is bounded by �(log, B) disk...

This paper presents a heuristic to solve the Multidimensional Multiple-choice Knapsack Problem (MMKP), a variant of the classical 0-1 Knapsack Problem. We apply a transformation technique to map the multidimensional resource consumption to single dimension. Convex hulls are constructed to reduce the search space to find the near-optimal solution of...

Abstract In this paper, we introduce a new approach to line drawing that attempts to maintain a uniform packing density of horizontal segments,to diagonal segments throughout the line. While the conventional,line drawing,algorithms,perform linear time computations to find the location of the pixels, our algorithm takes logarithmic time. Also, exper...

In this paper we present a generalized heapsort algorithm and its worst-case complexity analysis. The weighted sum of the number of comparisons and movements has been defined as a measure of the complexity. Theoretical analysis suggests that, by this criterion, 3-heap should be optimal in the worst case, contradicting the findings of A. Paulik (Pau...

Symbolic substitution, a parallel processing technique, has been proposed in computing literature to perform fast, carry-free addition of numbers. Several algorithms and corresponding symbolic substitution tables have been developed for addition of two numbers represented in binary, modified signed digit (MSD), and canonical modified signed digit (...

A Hamiltonian cycle is a spanning cycle in a graph, i.e., a cycle through every vertex, and a Hamiltonian path is a spanning path. In this paper we present two theorems stating sufficient conditions for a graph to possess Hamiltonian cycles and Hamil-tonian paths. The significance of the theorems is discussed, and it is shown that the famous Ore's...

This paper deals with the complexity issues of some new interesting spanning tree problems. Here we define some new spanning tree problems by imposing various constraints and restrictions on graph parameters and present relevant results. Also we introduce a new notion of "set version" of some decision problems having integer K < |V | as a parameter...

Among the different algorithms that have been proposed for the conversion of a binary number to its canonical modified signed-digit representation, the Reitwiesner's algorithm has been the most cited and regarded as the most efficient one in the computing literature. In this paper, however, we present two new conversion algorithms that are computat...

Search trees, specially binary search trees, are very important data structures thatcontributed immensely to improved performance of different search algorithms. In this paper, we express certain parameters of search trees in terms of Stirling numbers. We also introduce two new inversion formulas relating Stirling numbers of the first and second ki...

This paper deals with the classical degree-bounded-spanning-tree problem. We define degree-d-bounded-spanning tree to be a spanning tree having no vertices of degree larger than d. The main result of this paper states that, if G =( V , E) is a connected graph having independence number d ,w hered ≥ 2, then G has a degree-d-bounded spanning tree. Al...

Dynamic or adaptive Huffman coding, proposed by Gallager [1] and extended by Knuth [21, can be used for compressing a continuous stream. Our proposal for accomplishing the same task is termed here as block Huffman coding. This is an easy and simple solution to compress continuous data by applying simple Huffman coding in blocks of data. For each bl...

In this paper, we present improved algorithms for min-max pair heaps introduced by S. Olariu et al. (A Mergeable Double-ended Priority Queue - The Comp. J. 34, 423-427, 1991). We also show that in the worst case, this structure, though slightly costlier to create, is better than min-max heaps of Strothotte (Min-max Heaps and Generalized Priority Qu...

In this paper a new exact string-matching algorithm with sub-linear average case complexity has been presented. Unlike other sub-linear string-matching algorithms it never performs more than n text character comparisons while working on a text of length n. It requires only O(mþs) extra pre-processing time and space, where m is the length of the pat...

The Restorable Dynamic Bandwidth Constrained Routing Problem is one of the most important research areas in Optical Networking Research and MPLS (Multi Protocol Label Switching) based networks. The problem aims at finding an optimal path with Bandwidth guarantees and fault tolerance capabilities and conforming to the QoS requirements of desired nat...

Development of Bangla application is relatively complex due to the complexities of Bangla character set. In case of Bangla Spell Checker application, detection of replacement errors, deletion errors, insertion errors and swap or transposition errors are to be handled effectively and efficiently because of their frequent occurrences. Proper coding s...

The shortest path problem is one of the most studied problems in computer science. In this paper, we suggest an algorithm for the solution of the single source shortest path problem in O(mk+n) time, where k, the ratio of maximum and minimum weights of the edges of the graph, is bounded by a constant, m is the number of edges and n is the number of...

The shortest path problem is one of the most studied problems in computer science. In a previous paper[7], we suggested an algorithm(the Augmented Shortest Path Algorithm) for the solution of the single source shortest path problem in O(mk+n) time, where k, the ratio of maximum and minimum weights of the edges of the graph, is bounded by a constant...

In this paper, lower and upper bounds for min-max pair heap construction has been presented. It has been shown that the construction of a min-max pair heap with n elements requires at least 2.07n element comparisons. A new algorithm for creating min-max pair heap has been devised that lowers the upper bound to 2.43n.

We present a new data structure for Huffman coding in which in addition to sending symbols in order of their appearance in the Huffman tree one needs to send codes of all circular leaf nodes (nodes with two adjacent external nodes), the number of which is always bounded above by half the number of symbols. We decode the text by using the memory eff...

In this paper we present a new sorting algorithm for heaps which can sort n (=2h+1-1) elements using no more than nlog2(n + 1)-(13/12)n-1 element comparisons in the worst case (including the heap creation phase). Experimental results show that this algorithm requires only nlog2(n+1) - 1.2n element comparisons in the average case. However it require...

In this paper we present a new data structure for double ended priority queue, called min-max fine heap, which combines the techniques used in fine heap and traditional min-max heap. The standard operations on this proposed structure are also presented, and their analysis indicates that the new structure outperforms the traditional one.

In this paper, we present a new mergesort algorithm which can sort n(= 2h+1 − 1) elements using no more than element comparisons in the worst case. This algorithm includes the heap (fine heap) creation phase as a pre-processing step, and for each internal node v, its left and right subheaps are merged into a sorted list of the elements under that n...

McDiarmid and Reed (1989) presented a variant of BOTTOM-UP-HEAPSORT which requires nlog2 n+n element comparisons (for n= 2 h+1-1) in the worst case, but requires an extra storage of n bits. Ingo Wegener (1992) has analyzed the average and worst case complexity of the algorithm which is very complex and long. In this paper we present a simplified co...

In this paper an iterative algorithm has been presented for calculating the square root of a real number with arbitrary order of convergence using formulae derived by applying binomial theorem. The primary objective is to reduce the number of division operations required.

The shortest path problem is one of the most studied problems in computer science. In this paper, we suggest an algorithm for the solution of the single source shortest path problem in O(mk+n) time, where k, the ratio of maximum and minimum weights of the edges of the graph, is bounded by a constant, m is the number of edges and n is the number of...

We make a correction to the calculation of mean seek time in a recent algorithm of intelligently positioned two headed disk systems. We also introduce a new two headed disk system with better mean seek time. 1 Introduction Two headed disk systems, as categorized in [3], may have (a) two arms autonomously controlled [2,4], (b) two arms and a single...

This paper presents a theorem that asserts that average edge length of the minimum spanning tree of a complete graph on nC 1 vertices is less than or equal to the average edge length of all the nC 1 minimum spanning trees of the induced graph onn vertices. The result is also in compliance with results given by Frieze and Steele. © 1999 Elsevier Sci...

In this paper we have observed and shown that ternary systems are more promising than the more traditional binary systems used in computers. In particular, ternary number system, heaps on ternary trees, and quicksort with 3 partitions do indicate some theoretical advantages over the more established binary systems. The magic Napierian e plays the c...

An iterative algorithm based on binary search has been presented for finding the mode of a sorted array and its frequency. Complexity of the algorithm has been deduced. Numerical experiments show its supremacy over the iterative implementation of Griffiths' algorithm.

The sections in this article are

A complete Bengali OCR is presented incorporating a novel hybrid approach to handwritten Bengali character recognition. The idea is to combine structural analysis and template matching techniques in order to recognise the handwritten Bengali characters. Handwritten Bengali characters are inherently cursive and there is an absence of well-defined st...

A technique of preprocessing an arbitrary system of linear equations has been presented. The solution scheme comprises two parts-the first reduces the problem to a symmetric positive definite system through multiplying corresponding matrix by its transpose using an algorithm of lower order like Strassen's scheme, and the second uses a standard iter...

We present a new algorithm for drawing lines in a raster device in which a suitable data structure has been chosen to avoid comparisons that are required, for example, in Bresenham's algorithm. Experimental results as well as clock cycles calculated theoretically suggest that this new algorithm outperforms the ones currently existing in the literat...

In this paper we present a new algorithm for solving the problem of ranking players in a round-robin tournament in which outcome of any match is a win or a loss. We also compare performance of our algorithm with that of ARRANGE and GIK algorithms for solving the same problem. Some theoretical properties of our algorithm have also been deduced.

This paper gives a recursive algorithm to solve the multi-peg Tower of Hanoi problem. The algorithm is based on the dynamic programming equation satisfied by the optimal value function, M(n, p), where M(n, p) denotes the minimum number of moves required to solve the problem with n discs and p pegs. This algorithm is the only one available, particul...

The binding energy of the ΛΛ hypernucleus ΛΛ31Si has been calculated variationally with a 28Si+n+Λ+Λ four-body model. The integrations have been carried out with the help of a Monte Carlo technique. Three different types of Λ-Λ and Λ-N potentials have been used. n-28Si and Λ-28Si potentials have been generated by folding the N-N and Λ-N potentials...

The binding energy of the ÎÎ hypernucleus {sub ÎÎ}³¹Si has been calculated variationally with a ²⁸Si+{ital n}+Î+Î four-body model. The integrations have been carried out with the help of a Monte Carlo technique. Three different types of Î-Î and Î-{ital N} potentials have been used. {ital n}-²⁸Si and Î-²⁸Si potentials have been generated...

This paper deals with the upper bound on the number of vertices of a d- polytope. An algorithm for constructing 4-polytopes with the maximum number of vertices is presented. The same algorithm yields d-polytopes with very large numbers of vertices.

It is shown that a sufficient condition for a nonnegative real symmetric matrix to be completely positive is that the matrix is diagonally dominant.

A set of easily verifiable sufficient conditions are derived for the existence of a positive (componentwise) solution of a linear nonhomogeneous system of equations in which the coefficient matrix can be partitioned into submatrices with positive ele- ments.

Easily verifiable sufficient conditions are obtained for the existence of a positive solution (componentwise) of a linear nonhomogeneous system of equations with positive coefficients.

In this paper we present a new data structure for implement- ing heapsort algorithm for pairs of which can be simultaneously stored and processed in a single register. Since time complexity of Carlsson type variants of heapsort has already achieved a leading coefficient of 1, concretely nlg n + nlglg n, and lower bound theory asserts that no compar...

DiskTrie is an efficient external-memory data structure for storing strings in mobile devices using flash memory. It supports Lookup and Prefix-Matching operations with a constant internal memory and linear processing requirements. The number of disk accesses it takes to search for a string among n unique finite strings is bounded by �(logn), while...

This paper improves the complexity of a newly introduced MST (Majority Spanning Tree) algorithm for ranking players of a round-robin tournament previously published.

A few researches have been carried out to efficiently recognize natural Bangla sentences. This paper proposes a technique to parse Bangla sentences in a new approach using context-free grammar rules that accepts all types of Bangla sentences including complex, compound, exclamatory and optative sentences. The proposed grammar also allows parsing al...