### Table 1 DP-based algorithm for solving traveling-salesman problems due to Held and Karp. The outermost loop is over the cardinality of subsets of already visited cities.

in Word reordering and a dynamic programming beam search algorithm for statistical machine translation

2003

"... In PAGE 8: ... The approach recursively evaluates the quantity D(C, j): D(C, j) := costs of the partial tour starting in city 1, ending in city j, and visiting all cities in C Subsets of cities C of increasing cardinality c are processed. The algorithm, shown in Table1 , works because not all permutations of cities have to be considered explicitly. During the computation, for a pair (C, j), the order in which the cities in C have been visited can be ignored (except j); only the costs for the best path reaching j has to be stored.... ..."

Cited by 10

### Table 1: Address Trace Characteristics. LocusRoute is a global router for VLSI standard cells, SA-TSP solves the traveling salesman problem using simulated annealing, PTHOR is a parallel logic simulator and Speech implements the lexical decoding stage of a speech interpretation language.

1992

"... In PAGE 5: ... The simulation of this application involved 5 million iterations over the array, during which the memory references and inter-reference timings were generated using a state machine. For the other four applications, the memory ref- erences were obtained from address traces that, as shown in Table1 , exhibit a varied distribution of mem- ory operations. The rst three of these are part of the SPLASH parallel benchmark set of traces that is available from Stanford University; a description of 1The contention for these locks is shown in the next section.... In PAGE 7: ... For the results presented below, round-robin distribution was used to evenly distribute the pages across all processor modules. Because the address traces listed in Table1 were ac- quired from machines dissimilar to Hector, it is only meaningful to compare the results for the di erent caching strategies and topologies; the absolute num- bers are not meaningful. In addition, the traces con- tain only memory references with no inter-reference timing information3.... ..."

Cited by 5

### Table 8: Results for the traveling salesman problem.

1996

"... In PAGE 32: ... To give an idea of the solution times, the 2392-city problem was solved in approximately 6 hours on a CYBER. As can be seen from Table8 , the lower bounds in the root node are very close to the optimal value which partly explains the success of cutting plane algorithms for the symmetric traveling salesman problem. When solving large instances a very... ..."

Cited by 4

### Table 8: Computational results for the traveling salesman problem.

1996

"... In PAGE 36: ...2 The Traveling Salesman Problem The literature on computational results for the traveling salesman problem is vast, and some of the results have already been shown in Section 3. To make the progress visual, we give in Table8 a list of \world records quot; with respect to the size of the instances. It should be noted that there are still some small instances unsolved, which indicates that small does not necessarily imply easy, and that large is not synonymous with di cult.... In PAGE 36: ... The instances can be found in the library TSPLIB, see Reinelt (1991). Table8 contains information on the number of \cities quot; n of the instances. For all instances a complete graph is assumed which means that the number of variables is equal to 1 2n(n ? 1).... In PAGE 36: ... To give an idea of the solution times, the 2392-city problem was solved in approximately 6 hours on a CYBER. As can be seen from Table8 , the lower bounds in the root node are very close to the optimal value which partly explains the success of cutting plane algorithms for the symmetric traveling salesman problem. When solving large instances a very advanced implementation is necessary, see Applegate et al.... ..."

Cited by 4

### Table 1: Results of Incremental Type Inference The man.ca program computes the Mandelbrot set using a dynamic algorithm. sim- ple.ca is the SIMPLE hydrodynamic simulation and p-i-c.ca is a particle-in-cell code. titest7.ca is a synthetic code designed to illustrate the algorithm apos;s e ectiveness and ap- pears in Appendix A. The mmult.ca program multiplies integer and oating point matrixes using a polymorphic library. poly.ca evaluates integer and oating point polynomials. The program tsp.ca solves the traveling salesman problem. quicksort.ca implements the quick- sort algorithm. queens.ca solves the N-queens problem, and t.ca computes a Fast Fourier Transform using a butter y network. All test cases were compiled with the standard CA prologue (240 lines of code) and are available along with the language manual [8] and the

1993

"... In PAGE 16: ... We have tested the type inference system on more than 20,000 lines of CA code. The results on a variety of real and synthetic programs appear in Table1 . precise refers to our incremental inference algorithm, palsberg refers to the inference algorithm in [14], and static refers to a basic constraint based inference which allocates exactly one type variable... ..."

Cited by 6

### Table 1: Results of Incremental Type Inference The man.ca program computes the Mandelbrot set using a dynamic algorithm. sim- ple.ca is the SIMPLE hydrodynamic simulation and p-i-c.ca is a particle-in-cell code. titest7.ca is a synthetic code designed to illustrate the algorithm apos;s e ectiveness and ap- pears in Appendix A. The mmult.ca program multiplies integer and oating point matrixes using a polymorphic library. poly.ca evaluates integer and oating point polynomials. The program tsp.ca solves the traveling salesman problem. quicksort.ca implements the quick- sort algorithm. queens.ca solves the N-queens problem, and t.ca computes a Fast Fourier Transform using a butter y network. All test cases were compiled with the standard CA prologue (240 lines of code) and are available along with the language manual [8] and the

1993

"... In PAGE 16: ... We have tested the type inference system on more than 20,000 lines of CA code. The results on a variety of real and synthetic programs appear in Table1 . precise refers to our incremental inference algorithm, palsberg refers to the inference algorithm in [14], and static refers to a basic constraint based inference which allocates exactly one type variable... ..."

Cited by 6

### Table 1: Computational results for the traveling salesman problem.

1996

"... In PAGE 15: ...perform well in general. To illustrate the progress made by using the polyhedral approach to solve the TSP,we present, in Table1 , the sizes of the largest instances that have been solved to optimality since 1954. Note that the values given in the column z root LP have been rounded to the nearest integer.... ..."

Cited by 4

### Table 1. Simulation Results on Traveling Salesman Problems

2007

"... In PAGE 4: ... To qualify how much better our proposed algorithm is making shorter routes than the traditional approaches, we have tested all of the algorithms with a large number of Traveling Salesman Problems up to 532 cities and all the simulations are run 10 times, and then compared to several known algorithms: Kohonen Networks [6] [7], a conventional genetic algorithm using a greedy crossover operator [8] [9]. The results of these simulations are summarized in Table1 . The first three columns indicate the problem ... In PAGE 5: ... And the symbol - means no convergence. From Table1 , we can see that the proposed algorithm has superior ability to search the shortest routes and cost less computation times. 5.... ..."

### Table 8. Table of results for the Traveling Salesman Problem.

1994

"... In PAGE 22: ... Ten runs were made for each problem. Table8... ..."

Cited by 10

### Table 1: Symmetric travelling salesman problems

2000

"... In PAGE 1: ... After each 100st generation the best elements are exchanged between the PNs. The results obtained are given in Table1 in the last column. The second column de- scribes the results obtained by a reimplementation of the same algorithm on a Sun UltraSparc1.... ..."

Cited by 1