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19 Cards in this Set
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approximate algorithm

describes any algorithm that produces solutions that are, most of the time, reasonably close to the optimal solution.

complete weighted graph

a graph whose edges have numbers attached to them where the numbers represent a variable

bruteforce algorithm

1) make a list of all possible Hamilton circuits of graph
2) calculate total weight for each circuit 3)choose optimal circuit OPTIMAL not efficient 
cheapestlink algorithm

1) pick cheapest edge available (if more than one, pick at random) and mark it
2)pick next cheapest edge and mark 3)continue picking and marking cheapest edge as long as it doest a) close to form a circuit b)create 3 edges out of a singe vertex 4) connect last two remaining vertices to close circuit EFFICIENT not optimal 
complete graph

a graph where every pair of vertices are joined by an edge

efficient algorithm

an algorithm for which the amount of computational effort required to implement the algorithm grows in some reasonable proportion with the size of the input to the problem

factorial

how many different ways there are of rearranging something
# Hamilton Circuits = (N1)! in a complete graph KN 
hamilton circuit

circuit that visits each vertex of a graph once and only once, and starts and ends on the same vertex
NOTE: a hamilton circuit automatically has a hamilton path 
hamilton path

path that visits each vertex of a graph once and only once
NOTE: you can have a hamilton path without a hamilton circuit 
inefficient algorithm

an algorithm for which the number of steps needed to carry it out grows disproportionately with the size of the problem

nearestneighbor algorithm

1) start at designated starting vertex, or if not designated, pick
2) from starting vertex, go to nearest neighbor (vertex which corresponding edge is smallest weight) 3) from each vertex, go to nearest neighbor, choosing only those unvisited vertices (more than one nearest neighbor pick one and continue until all vertices visited) 4) from last vertex, return to starting vertex EFFICIENT 
optimal algorithm

an algorithm that when correctly implemented, is guaranteed to produce an optimal solution

relative error

a relative measure of how far a given Hamilton circuit is from the optimal circuit
given by E= (W  Opt =)/Opt where W is weight of any given circuit and Opt is the weight of the optimal circuit. 
repetitive nearestneighbor algorithm

1) let X be any vertex. Find nearest neighbor circuit using X as starting vertex and calculate total cost of circuit
2) repeat process w/each other vertex of graph as start 3) of nearest neighbor circuits, keep the best one. If there is a designated starting vertex, rewrite circuit using that vertex as reference pt. EFFICIENT 
traveling salesman problem

finding the best, cheapest route of visiting a number of cities

weighted graph

any graph whose edges have numbers attached to them

weight

numbers attached to edges

Finding edges in KN

N(N1)/2edges

# of Hamilton circuits

(N1)!
