scholarly journals Matroids And Greedy Algorithms. A Deeper Justification of Using Greedy Approach To Find A Maximal set of a Matroid

2017 ◽  
Vol 16 (2) ◽  
pp. 48
Author(s):  
Syed Aqib Haider
Keyword(s):  
Greedy Algorithm ◽  
Local Level ◽  
Greedy Algorithms ◽  
Optimal Solution ◽  
Independent Set ◽  
Computation Time ◽  
Optimal Choice ◽  
Greedy Approach ◽  
The Greedy Algorithm ◽  
Selection Of

<p>Greedy algorithms are used in solving a diverse set of problems in small computation time. However, for solving problems using greedy approach, it must be proved that the greedy strategy applies. The greedy approach relies on selection of optimal choice at a local level reducing the problem to a single sub problem, which actually leads to a globally optimal solution. Finding a maximal set from the independent set of a matroid M(S, I) also uses greedy approach and justification is also provided in standard literature (e.g. Introduction to Algorithms by Cormen et .al.). However, the justification does not clearly explain the equivalence of using greedy algorithm and contraction of M by the selected element. This paper thus attempts to give a lucid explanation of the fact that the greedy algorithm is equivalent to reducing the Matroid into its contraction by selected element. This approach also provides motivation for research on the selection of the test used in algorithm which might lead to smaller computation time of the algorithm.</p>

scholarly journals Komparasi Algoritma Cheapest Insertion Heuristic (CIH) Dan Greedy Dalam Optimasi Rute Pendistribusian Barang

2020 ◽  
Vol 2 (2) ◽  
pp. 31-39
Author(s):  
L.Virginayoga Hignasari
Keyword(s):  
Qualitative Research ◽  
Greedy Algorithm ◽  
Greedy Algorithms ◽  
Advantages And Disadvantages ◽  
Shortest Route ◽  
The Difference ◽  
The Greedy Algorithm ◽  
Insertion Heuristic ◽  
Selection Of

This study was aimed to compare algorithms that can effectively provide better solutions related to the problem of determining the shortest route in the distribution of goods. This research was a qualitative research. The object of research was the route of shipping goods of a business that is engaged in printing and convection. The algorithms compared in this study were Cheapest Insertion Heuristic (CIH) and Greedy algorithms. Both algorithms have advantages and disadvantages in finding the shortest route. From the results of the analysis using these two algorithms, the Cheapest Insertion Heuristic (CIH) and Greedy algorithm can provide almost the same optimization results. The difference was only the selection of the journey. The strength of the Greedy algorithm was that the calculation steps are simpler than the Cheapest Insertion Heuristic (CIH) algorithm. While the disadvantage of the Greedy algorithm was that it is inappropriate to find the shortest route with a relatively large number of places visited. The advantage of the Cheapest Insertion Heuristic (CIH) algorithm was that this algorithm is still stable, used for the relatively large number of places visited. While the lack of Cheapest Insertion Heuristic (CIH) algorithm was a complicated principle of calculation and was relatively longer than the Greedy algorithm.

scholarly journals Randomized Greedy Algorithms for Independent Sets and Matchings in Regular Graphs: Exact Results and Finite Girth Corrections

2009 ◽  
Vol 19 (1) ◽  
pp. 61-85 ◽  
Author(s):  
DAVID GAMARNIK ◽  
DAVID A. GOLDBERG
Keyword(s):  
Greedy Algorithm ◽  
Greedy Algorithms ◽  
Independent Set ◽  
Independent Sets ◽  
Simple Expression ◽  
Regular Graphs ◽  
Bounded Degree ◽  
Constant Degree ◽  
Image Position ◽  
The Greedy Algorithm

We derive new results for the performance of a simple greedy algorithm for finding large independent sets and matchings in constant-degree regular graphs. We show that forr-regular graphs withnnodes and girth at leastg, the algorithm finds an independent set of expected cardinalitywheref(r) is a function which we explicitly compute. A similar result is established for matchings. Our results imply improved bounds for the size of the largest independent set in these graphs, and provide the first results of this type for matchings. As an implication we show that the greedy algorithm returns a nearly perfect matching when both the degreerand girthgare large. Furthermore, we show that the cardinality of independent sets and matchings produced by the greedy algorithm inarbitrarybounded-degree graphs is concentrated around the mean. Finally, we analyse the performance of the greedy algorithm for the case of random i.i.d. weighted independent sets and matchings, and obtain a remarkably simple expression for the limiting expected values produced by the algorithm. In fact, all the other results are obtained as straightforward corollaries from the results for the weighted case.

Greedy Algorithms

1995 ◽  
Author(s):  
Raymond Greenlaw ◽  
H. James Hoover ◽  
Walter L. Ruzzo
Keyword(s):  
Greedy Algorithms ◽  
Independent Set ◽  
Independent Sets ◽  
Case Finding ◽  
Sequential Algorithm ◽  
Maximal Independent Set ◽  
Maximum Independent Set ◽  
Greedy Method ◽  
Numerical Order ◽  
Selection Of

We consider the selection of two basketball teams at a neighborhood playground to illustrate the greedy method. Usually the top two players are designated captains. All other players line up while the captains alternate choosing one player at a time. Usually, the players are picked using a greedy strategy. That is, the captains choose the best unclaimed player. The system of selection of choosing the best, most obvious, or most convenient remaining candidate is called the greedy method. Greedy algorithms often lead to easily implemented efficient sequential solutions to problems. Unfortunately, it also seems to be that sequential greedy algorithms frequently lead to solutions that are inherently sequential — the solutions produced by these algorithms cannot be duplicated rapidly in parallel, unless NC equals P. In the following subsections we will examine this phenomenon. We illustrate some of the important aspects of greedy algorithms using one that constructs a maximal independent set in a graph. An independent set is a set of vertices of a graph that are pairwise nonadjacent. A maximum independent set is such a set of largest cardinality. It is well known that finding maximum independent sets is NP-hard. An independent set is maximal if no other vertex can be added while maintaining the independent set property. In contrast to the maximum case, finding maxima? independent sets is very easy. Figure 7.1.1 depicts a simple polynomial time sequential algorithm computing a maximal independent set. The algorithm is a greedy algorithm: it processes the vertices in numerical order, always attempting to add the lowest numbered vertex that has not yet been tried. The sequential algorithm in Figure 7.1.1, having processed vertices 1,... , j -1, can easily decide whether to include vertex j. However, notice that its decision about j potentially depends on its decisions about all earlier vertices — j will be included in the maximal independent set if and only if all j' less than j and adjacent to it were excluded.

scholarly journals Greedy, A-Star, and Dijkstra’s Algorithms in Finding Shortest Path

2021 ◽  
Vol 2 (1) ◽  
pp. 45-52
Author(s):  
Muhammad Rhifky Wayahdi ◽  
Subhan Hafiz Nanda Ginting ◽  
Dinur Syahputra
Keyword(s):  
Greedy Algorithm ◽  
Shortest Path ◽  
Optimal Solution ◽  
The Other ◽  
Complex Data ◽  
Dijkstra’S Algorithm ◽  
Dijkstra's Algorithm ◽  
The Greedy Algorithm ◽  
Better Than

The problem of finding the shortest path from a path or graph has been quite widely discussed. There are also many algorithms that are the solution to this problem. The purpose of this study is to analyze the Greedy, A-Star, and Dijkstra algorithms in the process of finding the shortest path. The author wants to compare the effectiveness of the three algorithms in the process of finding the shortest path in a path or graph. From the results of the research conducted, the author can conclude that the Greedy, A-Star, and Dijkstra algorithms can be a solution in determining the shortest path in a path or graph with different results. The Greedy algorithm is fast in finding solutions but tends not to find the optimal solution. While the A-Star algorithm tends to be better than the Greedy algorithm, but the path or graph must have complex data. Meanwhile, Dijkstra's algorithm in this case is better than the other two algorithms because it always gets optimal results.

scholarly journals Comparison of Dynamic Programming Algorithm and Greedy Algorithm on Integer Knapsack Problem in Freight Transportation

2018 ◽  
Vol 5 (1) ◽  
pp. 49 ◽  
Author(s):  
Global Ilham Sampurno ◽  
Endang Sugiharti ◽  
Alamsyah Alamsyah
Keyword(s):  
Dynamic Programming ◽  
Greedy Algorithm ◽  
Knapsack Problem ◽  
Dynamic Programming Algorithm ◽  
Optimal Solution ◽  
Freight Transportation ◽  
Total Weight ◽  
Knapsack Problems ◽  
Programming Algorithm ◽  
Selection Of

At this time the delivery of goods to be familiar because the use of delivery of goods services greatly facilitate customers. PT Post Indonesia is one of the delivery of goods. On the delivery of goods, we often encounter the selection of goods which entered first into the transportation and  held from the delivery. At the time of the selection, there are Knapsack problems that require optimal selection of solutions. Knapsack is a place used as a means of storing or inserting an object. The purpose of this research is to know how to get optimal solution result in solving Integer Knapsack problem on freight transportation by using Dynamic Programming Algorithm and Greedy Algorithm at PT Post Indonesia Semarang. This also knowing the results of the implementation of Greedy Algorithm with Dynamic Programming Algorithm on Integer Knapsack problems on the selection of goods transport in PT Post Indonesia Semarang by applying on the mobile application. The results of this research are made from the results obtained by the Dynamic Programming Algorithm with total weight 5022 kg in 7 days. While the calculation result obtained by Greedy Algorithm, that is total weight of delivery equal to 4496 kg in 7 days. It can be concluded that the calculation results obtained by Dynamic Programming Algorithm in 7 days has a total weight of 526 kg is greater when compared with Greedy Algorithm.

scholarly journals Optimizing Tool Path Sequence Of Plasma Cutting Machine Using TSP Approach

2020 ◽  
Vol 184 ◽  
pp. 01037
Author(s):  
Shreeyash Sonawane ◽  
Pallavi Patil ◽  
Ramkrishna Bharsakade ◽  
Pankaj Gaigole
Keyword(s):  
Cycle Time ◽  
Tool Path ◽  
Energy Savings ◽  
Cutting Tool ◽  
Optimal Solution ◽  
Optimal Choice ◽  
Plasma Cutting ◽  
Optimal Sequence ◽  
Cutting Head ◽  
The Greedy Algorithm

The paper consists of optimizing the total distance traveled by the Plasma Cutting Tool Head. It is cross-functional implementation traveling salesman problem to the core manufacturing process of plasma cutting. This study contributes to reduce the total rapid traverse length (Total Through-Air Travelled Distance) by the cutting tool (Plasma Beam), which is totally a non-productive as well as non-value adding process contributing to the machine running costs and cycle time of the product directly and indirectly. For deriving this optimal sequence for the plasma cutting head, a heuristic algorithm is used. This algorithm calculates an optimal solution for a problem creating the best possible sequence. The greedy algorithm follows the problem-solving heuristics of making a locally optimal choice at every stage, finally integrating a globally optimal solution. Hence after deducing this optimal sequence and when accompanied by the Plasma Cutting tool, it resulted in the least distance traveled, contributing to minimizing cost and energy savings of the machine and simultaneously reducing the total traveled distance and similarly the cycle time.

A New Algorithm Based Orthogonal Arrays for Design of Experiment on Nonlinear Functions

2013 ◽  
Vol 284-287 ◽  
pp. 2980-2985
Author(s):  
Hsin Chuan Kuo ◽  
Chao Tsung Lee ◽  
Ching Hai Lin
Keyword(s):  
Exact Solution ◽  
Optimal Solution ◽  
Computation Time ◽  
Orthogonal Arrays ◽  
Superior Performance ◽  
Final Solution ◽  
Nonlinear Functions ◽  
Full Factorial ◽  
Final Selection ◽  
Selection Of

A new algorithm based orthogonal arrays was developed to determine the optimal solution amid all the optional settings for a new initiated device. The proposed algorithm begins with several successive orthogonal arrays and ends with a full factorial array. After each orthogonal array is accomplished, the algorithm employs variance analyses to screen the dominating variable from among all the current variables and then determines the best level of the dominating variable. Here, after successive orthogonal arrays were completed, the number of unfixed variables was gradually reduced to a number that was small enough to feasibly conduct a full factorial array, resulting in the final selection of the problem’s optimum setting. We verified the proposed algorithm by first applying it to the Rosenbrock function.To distinguish the superior performance of the proposed algorithm in comparison with other design of experiments approaches, we experimented with three different problems with non-interactive or interactive variables. The results show that the proposed method not only provides a final solution that is identical to the problem’s exact solution but also that the computation time in comparison with that required by a full factorial array drops drastically as the number of variables increases.

scholarly journals On Factors of Independent Transversals in $k$-Partite Graphs

2021 ◽  
Vol 28 (4) ◽  
Author(s):  
Raphael Yuster
Keyword(s):  
Bipartite Graph ◽  
Greedy Algorithm ◽  
Pairwise Disjoint ◽  
Independent Set ◽  
Single Vertex ◽  
Hall's Theorem ◽  
Hall’S Theorem ◽  
The Greedy Algorithm

A $[k,n,1]$-graph is a $k$-partite graph with parts of order $n$ such that the bipartite graph induced by any pair of parts is a matching. An independent transversal in such a graph is an independent set that intersects each part in a single vertex. A factor of independent transversals is a set of $n$ pairwise-disjoint independent transversals. Let $f(k)$ be the smallest integer $n_0$ such that every $[k,n,1]$-graph has a factor of independent transversals assuming $n \geqslant n_0$. Several known conjectures imply that for $k \geqslant 2$, $f(k)=k$ if $k$ is even and $f(k)=k+1$ if $k$ is odd. While a simple greedy algorithm based on iterating Hall's Theorem shows that $f(k) \leqslant 2k-2$, no better bound is known and in fact, there are instances showing that the bound $2k-2$ is tight for the greedy algorithm. Here we significantly improve upon the greedy algorithm bound and prove that $f(k) \leqslant 1.78k$ for all $k$ sufficiently large, answering a question of MacKeigan.

FAIR RESOURCE ALLOCATION IN A SIMPLE MULTI-AGENT SETTING: SEARCH ALGORITHMS AND EXPERIMENTAL EVALUATION

2005 ◽  
Vol 14 (06) ◽  
pp. 887-899 ◽  
Author(s):  
PARASKEVI RAFTOPOULOU ◽  
MANOLIS KOUBARAKIS ◽  
KOSTAS STERGIOU ◽  
PETER TRIANTAFILLOU
Keyword(s):  
Resource Allocation ◽  
Greedy Algorithm ◽  
Optimal Solution ◽  
Search Algorithms ◽  
Phase Transition Behavior ◽  
Exponential Time ◽  
Anytime Algorithm ◽  
Multi Agent ◽  
The Relationship ◽  
The Greedy Algorithm

We study the problem of fair resource allocation in a simple cooperative multi-agent setting where we have k agents and a set of n objects to be allocated to those agents. Each object is associated with a weight represented by a positive integer or real number. We would like to allocate all objects to the agents so that each object is allocated to only one agent and the weight is distributed fairly. We adopt the fairness index popularized by the networking community as our measure of fairness, and study centralized algorithms for fair resource allocation. Based on the relationship between our problem and number partitioning, we devise a greedy algorithm for fair resource allocation that runs in polynomial time but is not guaranteed to find the optimal solution, and a complete anytime algorithm that finds the optimal solution but runs in exponential time. Then we study the phase transition behavior of the complete algorithm. Finally, we demonstrate that the greedy algorithm actually performs very well and returns almost perfectly fair allocations.

scholarly journals Hybrid Invasive Weed Optimization with Greedy Algorithm for an Energy and Deadline Aware Scheduling in Cloud Computing

2019 ◽  
Vol 8 (12) ◽  
pp. 1354-1359
Keyword(s):  
Cloud Computing ◽  
Greedy Algorithm ◽  
Greedy Algorithms ◽  
Population Based ◽  
Task Completion ◽  
Network Access ◽  
Invasive Weed Optimization ◽  
Invasive Weed ◽  
Resource Pooling ◽  
The Greedy Algorithm

Cloud computing is being envisioned to be the computing paradigm of the next generation primarily for its advantages of on-demand services, risk transference, resource pooling that is independent of location and ubiquitous network access. Service quality is allocated using various resources in the scheduling process. The deadline refers to the time period from task submission until task completion. An algorithm that has good scheduling attempts at keeping the task executed inside the constraint of the deadline. The Genetic Algorithm (GA) is a common metaheuristic that is used often in literature for procuring solutions that are either optimal or near-optimal. The Invasive Weed Optimization (IWO) is an evolutionary algorithm that is population-based with certain interesting specifications like creations of offspring that are based on the levels of fitness of the parents which increases the size of the population and generates new population by making use of the best among parents and the best among off-springs. The Greedy Algorithms will construct an object that is globally best by means of continuously choosing the option that is locally the best. In this work, a hybrid GA with the Greedy Algorithm and a Hybrid IWO with the Greedy Algorithm that has been proposed for the energy and the deadline-aware scheduling in cloud computing.

Sign in / Sign up

Export Citation Format

Share Document