The input to this problem is a sequence of n points p1; ; pn in the Euclidean plane. You are to nd the shortest routes for two taxis to service these requests in order. The two taxis start at the origin p1. If a taxi visits a point pi before pj then it must be the case that i < j. Each point must be visited by one of the two taxis. The cost of a routing is the total distance traveled by the rst taxi plus the total distance traveled by the second taxi. Design an ecient dynamic programming algorithm to nd the minimum cost routing such that each point is covered by one of the two taxis

The input to this problem is a sequence of n points p1; ; pn in the Euclidean plane. You are to nd the shortest routes for two taxis to service these requests in order. The two taxis start at the origin p1. If a taxi visits a point pi before pj then it must be the case that i < j. Each point must be visited by one of the two taxis. The cost of a routing is the total distance traveled by the rst taxi plus the total distance traveled by the second taxi. Design an ecient dynamic programming algorithm to nd the minimum cost routing such that each point is covered by one of the two taxis

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter20: Queuing Theory

Section20.11: The M/g/s/gd/s/∞ System (blocked Customers Cleared)

Problem 4P

See similar textbooks

Similar questions

(you should achieve O(n) time)When Bob wants to send Alice a message M on the Internet, he breaks M into n data packets, numbers the packets consecutively, and injects them into the network. When the packets arrive at Alice’s computer, they may be out of order, so Alice must assemble the sequence of n packets in order before she can be sure she has the entire message. Describe an efficient scheme for Alice to do this. What is the running time of this algorithm?
When Bob wants to send Alice a message M on the Internet, he breaks M into n data packets, numbers the packets consecutively, and injects them into the network. When the packets arrive at Alice’s computer, they may be out of order, so Alice must assemble the sequence of n packets in order before she can be sure she has the entire message. Describe an efficient scheme for Alice to do this. What is the running time of this algorithm? From Data Structures and Algorithms C-7.56
Dijkstra’s algorithm computes the least-cost path from one node (the source, which we will refer to as ?u) to all other nodes in the network. Dijkstra’s algorithm is iterative and has the property that after the k-th iteration of the algorithm, the least-cost paths are known to k destination nodes, and among the least-cost paths to all destination nodes, these k paths will have the k smallest costs. Let - D(v): cost of the least-cost path from the source node to destination ?v as of this iteration of the algorithm. - p(v): previous node (neighbor of v) along the current least-cost path from the source to v. - N′: a subset of nodes; v is in N′ if the least-cost path from the source to ?v is definitely known. The centralized routing algorithm consists of an initialization step followed by a loop. The number of times the loop is executed is equal to the number of nodes in the network. Upon termination, the algorithm will have calculated the shortest paths from the source…
Consider the following shortest path problem. Find the total distance of shortest route from Node 1 to Node 4. From To Node Node Distance 1 2 250 1 3 400 1 4 600 2 3 50 2 4 300 3 4 200 a. 600 b. 50 c. 750 d. 500 e. 550
Delivery person wants to deliver the courier from senders location to receivers location. There exists a path from area1 to area2 but there is no direct route between area1 and area5. This routes are bidirectional. To reach area5, delivery person can take any route like 1-2-4-5 or 1-2-3-4-5. Please provide python code to find all possible routes in between area1 and area5 in the graph using the given matrix. I have a doubt in this question of finding all routes in this graph from 1 to 5 i.e 1-2-3-4-5 and 1-2-4-5. I tried solving it but getting an Index Error in my python code. Please provide python code of finding all routes from 1 to 5 in the given graph using this matrix.
b.) Write an integer programming formulation to find the second-shortest path from 1 to 8 in this network. (Hint: if the shortest path is not available, the second-shortest path becomes the shortest path.)
Shouldn't the number of paths from D to E be C(6,2) and from E to C be C(4,2)?
1. What is the value of ω(2, 5)? Answer: 7 2. What is the value of δ(4, 3) Answer: 7 3. What is the value of δ(6,3)? Answer: 4 4. For the following four questions, consider the single-source all-destinations shortest path with source node v_4. Regardless of their efficiency, which algorithms can find the answer of the problem above? Choose all that apply. a. Bellman-Ford b. Dijkstra c. Floyd-Warshall 5. What is the depth of the shortest path tree? The depth is the number of edges along the longest path from the root to a leaf node. Answer: 6. What is the value of v_1∙π? Answer: 7. What is the value of v_3∙d? Answer: For the following five questions, consider Floyd-Warshall algorithm for all-pairs shortest path and answer the following questions. Type in a numeric answer. If the answer is infinity, type "inf". 8. What is the value of d^2 (v_4,v_1 )? Answer: 9. What is the value of d^5 (v_4,v_1 )? Answer: 10. What is the value of d^1 (v_5,v_4 )? Answer: 11. d^k (i,j)=δ(i,j) only if…
The shortest route technique might be logically used for a. finding the shortest travel distance between two points. b. finding the most scenic route to allow travel to several places during a trip on spring break. c. finding the longest time to travel between two points. d. none of the answers presented apply. e. connecting all the points of a network together while minimizing the distance between them.
Consider a bipartite network with N1 and N2 nodes in the two sets. What is the maximum number of links Lmax the network can have? How many links cannot occur compared to a non-bipartite network of sizeN=N1 +N2? If N1<<N2, what can you say about the network density, that is the total number of links over the maximum number of links, Lmax? Find an expression connecting N1, N2 and the average degree for the two sets in the bipartite network, 〈k1〉 and 〈k2〉.
Based on the given data: a) Determine the total number of paths in the precedence network b) Which of the following is NOT one of the paths? Explain ABC GHI BGI GEF c) What is the duration of the CRITIAL PATH(s)? d) What is the duration of the SHORTEST PATH?
Let's start by looking into routing in more detail. Differentiate between these two widely-used routing strategies.