R.G. Parker and R.L. Rardin. Guaranteed performance heuristics for the bottleneck traveling salesman problem. Oper. Res. Letters, 2(6):269--272, 1984.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....endpoints, then minimizing the bottleneck cost in a network corresponds to minimizing the maximum distance traveled in a single hop in the network. Problems in which the objective is to keep the bottleneck cost low are termed bottleneck problems and these have also received considerable attention [20, 72, 123]. In many applications that arise in real world situations, the network to be built is required to minimize more than one of these cost measures simultaneously. Recent papers have identified many problems [8, 85, 89, 161] wherein multiple objectives are specified in the statement of the problem. ....

.... effort has been dedicated to the study of minimum cost network problems: e.g. spanning trees [4, 98, 127] TSPs [48, 100] Steiner trees [74, 156, 164] generalized Steiner trees [2] and even more general one connected networks [52, 60, 154] Bottleneck problems have been investigated in [20, 72, 123]. Multi objective approximations While there has been much work on finding minimum cost networks for each of the cost measures that we simultaneously minimize, there has been relatively little work on approximations for multiobjective network design. In this direction, Bar Ilan and Peleg [8] ....

R. G. Parker, and R. L. Rardin, "Guaranteed performance heuristic for the bottleneck traveling salesman problem," Oper. Res. Lett. 6, pp. 269-272, (1982).

....edge reflects the geographical distance between its endpoints, then minimizing the bottleneck cost in a network corresponds to minimizing the maximum distance traveled in a single hop in the network. Such problems are termed bottleneck problems and these have also received considerable attention [14, 25]. Finding a network of sufficient generality and of minimum cost with respect to each one of these measures can be shown to be NP complete [11] Hence much of the work mentioned above focuses on approximation algorithms for each of these problems. However, in applications that arise in real world ....

....1.7 There is a polynomial time algorithm that, given a undirected graph with edge costs obeying the triangle inequality, outputs a TSP tour whose total cost is at most four times optimum and whose bottleneck cost is at most eight times optimum. We note that the techniques of Parker and Rardin [25] and subsequently Hochbaum and Shmoys [14] apply to approximate the bottleneck cost of the TSP within a factor of two of the optimum. Similarly, the techniques of Rosenkrantz, Stearns and Lewis [28] apply to approximate the total cost of the TSP within twice the optimum. However, the theorem above ....

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R. G. Parker, and R. L. Rardin, "Guaranteed performance heuristic for the bottleneck traveling salesman problem," Oper. Res. Lett. 6, pp. 269-272, (1982).

....Fleischner proved that the square of a 2 node connected graph is Hamiltonian [6, 7] and Lau, in his Ph.D. thesis, provided a constructive proof [9, 10] that finds a Hamiltonian cycle in O(n 2 ) time. We note that Fleischner s result is applied to the tsp in a similar way by Parker and Rardin [14], who show a 2 approximation for the bottleneck tsp. Lemma 1 Any Hamiltonian cycle in S 2 yields an 8 approximation. Proof. The graph S has weight at most 2 Delta opt. Notice that it is not sufficient for the analysis to bound the total weight of the edges in S 2 , because the weight could ....

R. Gary Parker and Ronald L. Rardin. Guaranteed performance heuristics for the bottleneck traveling salesman problem. Operations Research Letters, 2(6):269--272, 1984.

....of G that span all the vertices in V . The bottleneck weight is defined as wB (G) min G 0 2F max e2G 0 w(e) and GB = V; EB ) is a Bottleneck Biconnected Spanning Subgraph of G if 8e 2 EB : w(e) wB (G) BBSS finds applications in solving the bottleneck traveling salesman problem [4][8], in communication networks [7] and in approximation algorithms of some hard bottleneck problems [5] 9] BBSS with vertices in the Euclidean plane has been studied by Chang, Tang and Lee [3] who propose an O(n 2 ) algorithm. For general graphs, Punnen and Nair [10] present an O(m n log n) ....

R G Parker and R L Rardin, Guaranteed performance heuristics for the bottleneck traveling salesman problem, Oper. Res. Lett. 2 (1984) 269272.

....Fleischner proved that the square of a 2 node connected graph is Hamiltonian [7, 8] and in his Ph.D. thesis Lau provided a constructive proof [11, 12] that finds a Hamiltonian cycle in polynomial time. We note that Fleischner s result is applied to the tsp in a simpler way by Parker and Rardin [17], who show a 2 approximation for the bottleneck tsp. Theorem 1 Algorithm tsp approx is a 4 approximation algorithm. Proof. The graph S has weight at most 2 Delta opt. The goal is to find a Hamiltonian cycle in S 2 that has low weight. Notice that it is not sufficient for the analysis to bound ....

R. Gary Parker and Ronald L. Rardin. Guaranteed performance heuristics for the bottleneck traveling salesman problem. Operations Research Letters, 2(6):269--272, 1984.

....to be NP complete, and no constant factor approximation algorithm can exist, unless P=NP. Assuming the edge lengths satisfy the triangle inequality, there exists an approximation algorithm to produce a tour whose longest edge has length that is at most twice the optimal, and this is best possible [18]. By similar techniques we obtain similar hardness results for the maximum scatter TSP (in edge weighted graphs) however, our approximation algorithm is very different from that given in [18] and neither algorithm works for the other problem. Another variant of the TSP that is potentially ....

.... produce a tour whose longest edge has length that is at most twice the optimal, and this is best possible [18] By similar techniques we obtain similar hardness results for the maximum scatter TSP (in edge weighted graphs) however, our approximation algorithm is very different from that given in [18], and neither algorithm works for the other problem. Another variant of the TSP that is potentially related to our work is the MAX TSP, in which the goal is to find a tour whose length is as long as possible. Several approximation algorithms exist for the MAX TSP (without any assumptions on the ....

[Article contains additional citation context not shown here]

R.G. Parker and R.L. Rardin. Guaranteed performance heuristics for the bottleneck traveling salesman problem. Oper. Res. Letters, 2(6):269--272, 1984.

....to be NP complete, and no constant factor approximation algorithm can exist, unless P=NP. Assuming the edge lengths satisfy the triangle inequality, there exists an approximation algorithm to produce a tour whose longest edge has length that is at most twice the optimal, and this is best possible [14]. By similar techniques we obtain similar hardness results for the maximum scatter TSP; however, our approximation algorithm is very different from that given in [14] and neither algorithm works for the other problem. Another variant of the TSP that is potentially related to our work is the MAX ....

.... approximation algorithm to produce a tour whose longest edge has length that is at most twice the optimal, and this is best possible [14] By similar techniques we obtain similar hardness results for the maximum scatter TSP; however, our approximation algorithm is very different from that given in [14], and neither algorithm works for the other problem. Another variant of the TSP that is potentially related to our work is the MAX TSP, in which the goal is to find a tour whose length is as long as possible. Several approximation algorithms exist for the MAX TSP (without any assumptions on the ....

[Article contains additional citation context not shown here]

R.G. Parker and R.L. Rardin. Guaranteed performance heuristics for the bottleneck traveling salesman problem. Oper. Res. Letters, 2(6):269--272, 1984.

....length of the longest edge in the tour. In graphs, the problem is NP complete [250] If the edge lengths do not satisfy the triangle inequality, then no constant factor approximation algorithm can exist, unless P=NP. If the edge lengths do satisfy the triangle inequality, then Parker and Rardin [321] have given a 2 approximation algorithm and shown that this is best possible (unless P=NP) For the geometric version of the problem, it is easy to show that the problem is NP hard, from the fact that Hamiltonian cycle in grid graphs is hard [250] In the maximum scatter TSP, the goal is to obtain ....

R. Parker and R. Rardin. Guaranteed performance heuristics for the bottleneck travelling salesman problem. Operations Research Letters, 2(6):269--272, 1984.

....to be NP complete, and no constant factor approximation algorithm can exist, unless P=NP. Assuming the edge lengths satisfy the triangle inequality, there exists an approximation algorithm to produce a tour whose longest edge has length that is at most twice the optimal, and this is best possible [8]. By similar techniques we obtain similar hardness results for the maximum scatter TSP; however, our approximation algorithm is very different from that given in [8] and neither algorithm works for the other problem. Another variant of the TSP that is potentially related to our work is the MAX ....

.... approximation algorithm to produce a tour whose longest edge has length that is at most twice the optimal, and this is best possible [8] By similar techniques we obtain similar hardness results for the maximum scatter TSP; however, our approximation algorithm is very different from that given in [8], and neither algorithm works for the other problem. Another variant of the TSP that is potentially related to our work is the MAX TSP, in which the goal is to find a tour whose length is as long as possible. Several approximation algorithms exist for the MAX TSP (without any assumptions on the ....

R.G. Parker and R.L. Rardin. Guaranteed performance heuristics for the bottleneck traveling salesman problem. Oper. Res. Letters, 2(6):269--272, 1984.

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R.G. Parker and R.L. Rardin. Guaranteed performance heuristics for the bottleneck traveling salesman problem. Oper. Res. Letters, 2(6):269--272, 1984.

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R.G. Parker and R.L. Rardin. Guaranteed performance heuristics for the bottleneck traveling salesman problem. Oper. Res. Lett., 2(6):269--272, 1984.

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