### 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. QoSMT problem with 2 rates. Runtime and approximation ratios of previ- ously known algorithms and of the algorithms given in this paper. In the runtime, n and m denote the number of nodes and edges in the original graph G = (V; E), respec- tively. Approximation ratios associated with polynomial-time approximation schemes are accompanied by a + to indicate that they approach the quoted value from above and do not reach this value in polynomial time.

2003

Cited by 5

### 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. 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: 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: Numerical comparisons of performance and CPU consumption on GAP apos;s with small N. The mean eld (MF) algorithm is checked against an exact depth- rst and branch-and-bound (DBB) method and a polynomial-time algorithm (MTG) for approximative solutions. All the test were made on a DEC Alpha 3000/400 workstation.

"... In PAGE 13: ... [8]). Table3 shows the result for small N problems where one can compare against the exact solutions. The numbers shown are averages over 1000 independent runs.... ..."

### Table 3: The maximal subalgebras of V which have a polynomial-time satis- ability problem.

"... In PAGE 16: ...emma 1.2 V-SAT(V23) is in P. Proof: Follows immediately from the de nition of V23 and the previous proposition. 2 Before we can show that the other algebras in Table3 have polynomial-time satis ability problems, we need an auxiliary de nition. De nition 1.... ..."