Math exam 1

What is the decreasing time list method?

if all the tasks are independent, then sort the paths into descending order, that order is the priority list

What is a tree?

it is connected and has no circuitz

What is a Hamiltonian circuit?

it visits each vertex once and only once and ends where it starts

How does first fit work?

put an item in the first bin, working from left to right in which it fits -if there is no such place, open a new bin

How do you create an Euler circuit?

re traverse the fewest number of edges in order to make all edges even valent

What is task scheduling?

schedule tasks so that the completion time is as early as possible

What is the edgewalker method?

start with upper left corner proceed clockwise around the edge of the graph if the vertex is even valent, do nothing and go to next vertex, if the vertex is odd valent, add edge to the next vertex

How do you find an optimal schedule?

sum up all the task times, dividde by the number of machines and round up

What is a real life example of an Euler circuit?

sweeping/plowing streets?

What two specifications determine whether or not an Euler circuit is present?

the graph must be connected and all vertices must be even valent

What is a critical path?

the longest path but shortest time for job to be completed in a digraph

What is the chromatic number of a graph?

the minimum number of colors needed to color all of the vertices of a graph

What are the 6 assumptions of task scheduling?

-all machines are identical -if a machine starts on a task, it works uninterupted until finished -No machine remains voluntarily idle -the task order is determined by the diagram -tasks can be arranged by a priority list -lower number machine has priority

What is vertex coloring?

-assign each vertex a color such that two vertices joined by the same edge are assigned different colors -use as few colors as possible

What are the steps to the Brute force method?

-find all hamiltonian circuits -choose the cheapest one

How does worst fit work?

-look at all open bins, put the item in the bin with the most room -if it doesnt fit in an open bin, open a new bin

What are the 6 bin packing methods?

-next fit -first fit -worst fit -next fit decreasinh -first fit decreasinh -worst fit decreasing

How does Next fit work?

-put items in a bin until there is no more room -open a new bin and put the item in that

How do you generate a priority list?

-remove first task from critical path and place at the end of a priority list -repeat until finished

What is a method to find a minimum cost spanning tree?

-sort edges in ascending order -add edges one by one such that it never forms a circuit -stop when all vertices connect

What are the steps to the sorted edges algorithm?

-sort edges in ascending order -add first 2 edges -add next edge as long as it doesn't make an odd valent vertex

What are the steps to the nearest neighbor algorithm?

-start at a vertex, go to nearest unvisited neighbor, repeat until all vertices are visited -return to start

What are the 3 methods to find minimum cost Hamiltonian circuits?

1)Brute force method 2) Nearest Neighbor method 3) sorted edges algorithm

What is the difference between Hamiltonian and Euler circuits?

Hamiltonian circuits deal with vertices and Euler circuits deal with edges

What is an euler circiut?

a circuit that covers each edge of a graph once and only once

What is a circuit?

a path that starts and ends at the same vertex

What is a spanning tree?

a tree that includes all vertices of the graph

What is a path?

connected sequence of edges showing a route on a graph that starts at a vertex and ends at a vertex

What are the restrictions of graphs?

each edge must connect to two different vertices, can be disconnected

What is an optimal schedule?

has the same time as the critical path