### Table 3 Polynomial-Time Algorithms Take Better Advantage of Technology

"... In PAGE 12: ... Even more illuminating is the effect that a technological breakthrough improving computer speed would have. Table3 (taken from Papadimitriou, Steiglitz 1982, p. 165) demonstrates how the size of the largest instance solvable increases when a computer (or an algorithm) with the tenfold speed becomes available: The most striking insight from such a comparison is that for a polynomial function this size multiplies by some factor while for an exponential function... ..."

### Table 5 Polynomial-Time Algorithms Take Better Advantage of Technology

"... In PAGE 10: ... Even more illuminating is the effect that a technological breakthrough improving computer speed would have. Table5 (taken from Papadimitriou, Steiglitz 1982, p. 165) demonstrates... ..."

### Table 1: Existence of Polynomial Time Learning Algorithms

1993

"... In PAGE 25: ...quivalence queries consist of arbitrary read-once formulas. Q.E.D. 9 Summary and remarks Table1 summarizes what is known of the computational di culty of learning monotone and arbitrary read-once formulas according to six types of learning protocols. The entries are discussed in order below.... ..."

Cited by 107

### Table 3: A polynomial-time algorithm for nding one (not necessarily optimal) MACPO

"... In PAGE 22: ... However, nding the optimal partial ordering \under reasonable optimality criteria quot; has been shown to be NP-hard [3]. In Table3 , we provide a polynomial-time algorithm for nding one (not necessarily optimal) minimal annotated consistent partial ordering. This algorithm is a variation on the one presented by [54], however, in order to handle conditional e ects, we must calculate the state between each step to determine whether the conditional e ects were active in the totally-ordered plan.... ..."

Cited by 2

### Table 2 Polynomial-Time Algorithms Take Better Advantage of Computation Time

"... In PAGE 12: ... Table2 (taken from Garey, Johnson 1979, p. 7) illustrates that in most cases polynomial algo- rithms make better use of given computer time because they are - at least up from a certain in- stance size - faster than exponential ones.... ..."

### Table 4 Polynomial-Time Algorithms Take Better Advantage of Computation Time

"... In PAGE 10: ... Table4 (taken from Garey, Johnson 1979, p. 7) illustrates that in most cases polynomial algo- rithms make better use of given computer time because they are - at least up from a certain in- stance size - faster than exponential ones.... ..."

### TABLE 3 Numerical Comparisons of Performance and CPU Consumption on GAPs with Small Al.The MFA Algorithm ia Checked Against an Exact DBB Method and a Polynomial-time Algorithm (MTG) for Approximate Solutiona. All the Testa were Carried Out on a DEC Alpha 30001400Workstation

1996

### Table 3. As shown in Table 3, the number of trees grows faster than Nk for any xed k. Thus the procedure of growing all trees is not a polynomial-time algorithm [7]. Day [3] has shown that in general the problem is NP-hard.

### Table 1: Survey of classes of graphs optimaly solvable in polynomial time.

1998

"... In PAGE 2: ... The MinLA problem is known to be NP-hard and its decision version is NP-complete [12]. However, there exist polynomial time algorithms to compute exact solutions for some partic- ular classes of graphs, which we survey in Table1 . Notwithstanding these positive results, the decision problem remains NP-complete even if the input graph is bipartite [11].... ..."

Cited by 5

### Table 1 summarizes our results. For conciseness, in the table below when we indicate that a problem is c-hard we mean that, unless NP = ZPP, no polynomial time algorithm can approximate it to within a factor of c.

"... In PAGE 5: ... Table1 : Approximation bounds and inapproximability results for each problem. 1.... ..."