Egbert Mujuni - Academia.edu (original) (raw)

Papers by Egbert Mujuni

DergiPark (Istanbul University), Jan 21, 2022

Bat Algorithm (BA) is one of the newest and promising nature inspired metaheuristics. Introduced ... more Bat Algorithm (BA) is one of the newest and promising nature inspired metaheuristics. Introduced by Yang in 2010, BA is a population method which is based on the echolocation characteristics of microbats. The original BA was proposed only for continuous optimization problems. Different approaches that use BA as basis for solving discrete optimization problem have been proposed. In this paper, a discrete bat algorithm version has been developed to solve the examination timetabling problem. Empirical study of the proposed algorithm was carried using data from the University of Dar es Salaam. The proposed algorithm demonstrated higher performance in comparison to a well known metaheuristic, Tabu Seach (TS).

Theoretical Computer Science, 2009

We consider computational problems on covering graphs with bicliques (complete bipartite subgraph... more We consider computational problems on covering graphs with bicliques (complete bipartite subgraphs). Given a graph and an integer k, the biclique cover problem asks whether the edge-set of the graph can be covered with at most k bicliques; the biclique partition problem is defined similarly with the additional condition that the bicliques are required to be mutually edge-disjoint. The biclique vertex-cover problem asks whether the vertex-set of the given graph can be covered with at most k bicliques, the biclique vertex-partition problem is defined similarly with the additional condition that the bicliques are required to be mutually vertex-disjoint. All these four problems are known to be NPcomplete even if the given graph is bipartite. In this paper we investigate them in the framework of parameterized complexity: do the problems become easier if k is assumed to be small? We show that, considering k as the parameter, the first two problems are fixed-parameter tractable, while the latter two problems are not fixed-parameter tractable unless P = NP.

Examination timetabling is an important operational problem in any academic institution. The prob... more Examination timetabling is an important operational problem in any academic institution. The problem involves assigning examinations and candidates to time periods and examination rooms while satisfying a set of specific constraints. An increased number of student enrollments, a wider variety of courses, and the growing flexibility of students' curricula have contributed to the growing challenge in preparing examination timetables. Since examination timetabling problems differ from one institution to another, in this paper we develop and investigate the impact of a two-phase heuristic that combines Graph-Colouring and Simulated Annealing at Sokoine University of Agriculture (SUA) in Tanzania. Computational results are presented which shows great improvement over the previous work on the same problem.

Mathematical theory and modeling, 2014

This paper aims to describe the mathematical formulation model and an exact optimal solution anal... more This paper aims to describe the mathematical formulation model and an exact optimal solution analyses for a school bus routing problem with small instance data. The formulated model has been used to compute the optimal solution of time spent by students at all bus stops, apart from that the bus stops are not necessary be linearly ordered. We also listed down five procedures of mathematical formulation model to reach an exact optimal solution for a school bus routing problem with small instance data. We assume that each bus has fixed pick up points, these generates the many possible routes for a bus, the number of routes that generated is equal to permutation of pick up points, for each route of a bus we computing the objective function and the route with smallest objective function value can be optimal route of a bus. The sample data from two schools located at Dar es Salaam are collected and validated in the model to shows the good performing of that model. The optimal solution re...

The problem of deciding whether the edge-set of a given graph can be partitioned into at most k c... more The problem of deciding whether the edge-set of a given graph can be partitioned into at most k cliques is well known to be NP-complete. In this paper we investigate this problem from the point of view of parameterized complexity. We show that this problem is fixed parameter tractable if we choose the number of cliques as parameter. In particular, we show that in polynomial time, a kernel bounded by k2 can be obtained, where k is the number of cliques. We also give an O(2((k+3) log k)/2n) algorithm for this problem in K4-free graphs.

This paper presents a graph coloring based algorithm for Examinations Timetabling Problem at Soko... more This paper presents a graph coloring based algorithm for Examinations Timetabling Problem at Sokoine University of Agriculture (SUA) in Tanzania. A Recursive Largest First algorithm for graph coloring is applied to find timeslots. We present a summary of results which indicates good performance.

Solid Waste Management is one of the critical environmental challenges for quick urban developing... more Solid Waste Management is one of the critical environmental challenges for quick urban developing countries. It involves a number of problems that requires optimization techniques for better decision making. These include the selection of collection points, disposal sites, and vehicle routing mechanisms. This paper addresses the problem of optimization of solid waste systems which involves the use of composting plants as a strategy in environmental management. A mathematical programming model is developed and tested on real data from Ilala Municipal in Dar es Salaam Tanzania. The formulated model resulted into lower transportation cost from sources to collection points, composting plant and landfill compared to previous results. Furthermore, it has been observed that construction of composting plants can provide extra income through sales of recyclable materials and compost manure and thereby reduce the overall system's running cost.

Many mathematical optimization problems from real-life applications are NP-hard, and hence no alg... more Many mathematical optimization problems from real-life applications are NP-hard, and hence no algorithm that solves them to optimality within a reasonable time is known. For this reason, metaheuristic methods are mostly preferred when their size is big. Many meta-heuristic methods have been proposed to solve various combinatorial optimization problems. One of the newly introduced metaheuristic methods is a bat-inspired algorithm, which is based on the echolocation behaviour of microbats. Bat algorithm (BA) and its variants have been used successfully to solve several optimization problems. However, from the No-free Lunch Theorem, it is known that there is no universal metaheuristic method that can solve efficiently all optimization problems. Thus, this study work focused on investigating the usefulness of BA in solving an optimization problem called Course Teaching Problem (CTP). Since BA was originally designed to solve continuous problems, and CTP is a combinatorial optimization p...

AKCE International Journal of Graphs and Combinatorics, 2017

Computer Engineering and Intelligent Systems, 2014

School bus routing is one of major problems facing many schools because student's transportation ... more School bus routing is one of major problems facing many schools because student's transportation system needs to efficient, safe and reliable. Because of this, the school bus routing problem (SBRP) has continued to receive considerable attention in the literature over the years. In short, SBRP seeks to plan an efficient schedule for a fleet of school buses where each bus picks up students from various bus stops and delivers them to their designated school while satisfying various constraints such as the maximum capacity of a bus, the maximum transport cost, the maximum travelling time of students in buses, and the time window to reach at school. Since school bus routing problems differ from one school to another, this paper aims to developing Simulated Annealing (SA) heuristic algorithms for solving formulating a mathematical model for solving the student bus routing problem. The objective of the model is to minimize amount of time students in the buses from the point where they pickup to the school. We illustrate the developed model using data from four schools located at Dar es salaam, Tanzania. We present a summary of results which indicates good performance of the model.

Mathematical Theory and Modeling, 2014

The problem of deciding whether the edge-set of a given graph can be partitioned into at most k c... more The problem of deciding whether the edge-set of a given graph can be partitioned into at most k cliques is well known to be NP-complete. In this paper we investigate this problem from the point of view of pa- rameterized complexity. We show that this problem is fixed parameter tractable if we choose the number of cliques as parameter. In particular, we show that in polynomial time, a kernel bounded by k2 can be obtained, where k is the number of cliques. We also give an O(2((k+3) log k)/2n) algorithm for this problem in K4-free graphs.

Mathematics in Computer Science, 2008

Smooth 4-regular hamiltonian graphs are generalizations of cycle plus triangles graphs. It has be... more Smooth 4-regular hamiltonian graphs are generalizations of cycle plus triangles graphs. It has been shown that both the independent set and 3-colorability problems are NP-Complete in this class of graphs. In this paper we show that these problems are fixed parameter tractable if we choose the number of inner cycles as parameter.

The problem of deciding whether the edge-set of a given graph can be partitioned into at most k c... more The problem of deciding whether the edge-set of a given graph can be partitioned into at most k cliques is well known to be NP-complete. In this paper we investigate this problem from the point of view of parameterized complexity. We show that this problem is fixed parameter tractable if we choose the number of cliques as parameter. In particular, we show that in polynomial time, a kernel bounded by k 2 can be obtained, where k is the number of cliques. We also give an O(2 ((k+3) log k)/2 n) algorithm for this problem in K 4-free graphs.

Given a graph and an integer k, the biclique cover problem asks whether the edge-set of the given... more Given a graph and an integer k, the biclique cover problem asks whether the edge-set of the given graph can be covered with at most k bicliques (complete bipartite subgraphs); the biclique vertex-cover problem asks whether the vertex-set of the given graph can be covered with at most k bicliques. Both problems are known to be NP-complete even if the given graph is bipartite. In this paper we investigate these two problems in the framework of parameterized complexity: do the problems become easier if k is assumed to be small? We show that, considering k as the parameter, the first problem is fixed-parameter tractable, while the second one is not fixed-parameter tractable unless P=NP.

DergiPark (Istanbul University), Jan 21, 2022

Theoretical Computer Science, 2009

Mathematical theory and modeling, 2014

AKCE International Journal of Graphs and Combinatorics, 2017

Computer Engineering and Intelligent Systems, 2014

Mathematical Theory and Modeling, 2014

The problem of deciding whether the edge-set of a given graph can be partitioned into at most k c... more The problem of deciding whether the edge-set of a given graph can be partitioned into at most k cliques is well known to be NP-complete. In this paper we investigate this problem from the point of view of pa- rameterized complexity. We show that this problem is fixed parameter tractable if we choose the number of cliques as parameter. In particular, we show that in polynomial time, a kernel bounded by k2 can be obtained, where k is the number of cliques. We also give an O(2((k+3) log k)/2n) algorithm for this problem in K4-free graphs.

Mathematics in Computer Science, 2008

The problem of deciding whether the edge-set of a given graph can be partitioned into at most k c... more The problem of deciding whether the edge-set of a given graph can be partitioned into at most k cliques is well known to be NP-complete. In this paper we investigate this problem from the point of view of parameterized complexity. We show that this problem is fixed parameter tractable if we choose the number of cliques as parameter. In particular, we show that in polynomial time, a kernel bounded by k 2 can be obtained, where k is the number of cliques. We also give an O(2 ((k+3) log k)/2 n) algorithm for this problem in K 4-free graphs.