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Questions and Answers
What is the goal of the uniform-profit restaurant location problem?
maximize number of restaurants open
What is the goal of the events scheduling problem?
maximize number of non-conflicting events
What is the goal of the fractional knapsack problem?
maximize value without exceeding bag capacity
What is a graph?
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In an undirected graph, edge (u,v) implies edge (v,u).
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In a directed graph, edge (u,v) implies edge (v,u).
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What is the degree of a vertex in a graph?
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What type of graph has a path from every vertex to every other vertex?
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What is true about a weighted graph?
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Which of the following problems is related to maximizing the value without exceeding capacity?
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Study Notes
Uniform-Profit Restaurant Location Problem
- The objective is to determine the optimal locations for restaurants to maximize profit.
- All restaurants are assumed to have the same profit potential.
Events Scheduling Problem
- The goal is to schedule a set of events, each with a start and end time, to maximize the number of events that can be scheduled without any overlap.
Fractional Knapsack Problem
- The goal is to maximize the total value of items selected from a set of items, each with a value and a weight, subject to a weight constraint.
- It is assumed that items can be partially selected.
Graphs
- A graph is a mathematical structure that represents relationships between objects.
- It consists of vertices (nodes) and edges connecting them.
Undirected Graphs
- In an undirected graph, edges represent undirected relationships.
- If edge (u, v) exists, it implies that vertex u is connected to vertex v, and vice versa (edge (v, u) also exists).
Directed Graphs
- In a directed graph, edges represent directed relationships.
- The existence of edge (u, v) only represents a connection from vertex u to vertex v.
- It does not necessarily imply the existence of edge (v, u).
Degree of a Vertex
- The degree of a vertex in a graph is the number of edges incident to it.
Connected Graphs
- A connected graph is a graph in which there exists a path from every vertex to every other vertex.
Weighted Graphs
- A weighted graph is a graph with a weight assigned to each edge.
- These weights can represent costs, distances, or other relevant information related to the edges.
Knapsack Problems
- The fractional knapsack problem is an example of a problem related to maximizing value without exceeding a capacity constraint.
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Description
This quiz covers essential concepts in graph algorithms and optimization problems, including the Uniform-Profit Restaurant Location Problem, Events Scheduling, and Fractional Knapsack Problem. Understand key definitions, variations of graphs, and constraints affecting optimization. Perfect for students looking to deepen their knowledge in computational problems.
