### Table 1.8: The time complexity of some fundamental graph drawing problems: trees. We denote with k a xed constant such that k 1. Class of Graphs Problem Time Complexity Source tree draw as the Euclidean minimum spanning tree of a set of points in the plane

1997

Cited by 14

### TABLE 44.3.3 The time complexity of some fundamental graph drawing problems: trees. k is a xed constant k 1. CLASS OF GRAPHS PROBLEM TIME COMPLEXITY tree draw as the Euclidean minimum span- ning tree of a set of points in the plane NP-hard

### Table 1: Comparison of the degree and running time of algorithms for some fundamental proximity query problems. A * denotes optimality. The technique introduced in this paper (point location in an implicit Voronoi diagram) outperforms previous methods and is optimal for 2D queries.

1997

"... In PAGE 2: ... However, we shall show that the latter method fails to achieve optimal degree because the search is based on predicates requiring 4b bits of precision; moreover, the high overhead of the search technique (which uses the hierarchical polytope representation [8]) casts some doubts on the practicality of the method. The main results of this work are summarized in Table1 . We show that previous methods for proxim- ity queries exhibit a sharp tradeo between degree and query time.... ..."

Cited by 33

### Table editing is generally not well supported in most environments,18 and it is not our purpose here to complain that markup does not do better.Rather,we wish to emphasize that the order of text inherited by markup is the fundamental reason for this problem. The overspecification of order can also be a problem ev enfor apparently benign nested texts. Consider the following fragment from a hypothetical repair manual that lists problems and their symptoms:

### Table 6: Hits by algorithmic problem, with implementation ratings

"... In PAGE 2: ... The world has been divided into a total of 75 fundamental algorithmic problems, partitioned among data structures, numerical algorithms, combinatorial algorithms, graph algorithms, hard problems, and computational geometry. See Table6 or http://www.... ..."

### Table 2: The algorithm COPRIME associated vectors given in Theorem A.1 below it becomes clear that our \look{ahead quot; strategy allows us to only encounter subproblems of type (9) with a corresponding well{conditioned matrix of coe cients Sk(a; b). In contrast, in the classical Euclidean algorithm there is no freedom of choosing a stepsize s, since we only encounter \small quot; triangular systems. In other words, we just take the rst existing UR, though the corresponding quantity j det U(0)j might be very small. Thus it might happen that some of the unimodular reductions of the Euclidean algorithm are ill{conditioned problems. This is the fundamental problem of using the Euclidean algorithm in a numerical setting: solutions are sometimes built upon solutions of ill-conditioned subproblems making the nal answers highly inaccurate. Our observation may be nicely illustrated with help of the polynomials a; b of Example 2.1. Here

"... In PAGE 8: ... We also introduce a set A f0; 1; 2; : : :; mg of indices of scaled UR accepted by our criterion. The order of computation is schematically described in Table2 . For further details and proofs we refer to [1, 7].... In PAGE 14: ... In other words, the ideal lt; a(k); b(k) gt; provides as much information with regard to coprimeness as the original one if j det U(k)(0)j is not too small. 2 5 Numerical Experiments The algorithm COPRIME of Table2 was implemented in Matlab and experiments were run in order to verify the predicted behavior. In this section we report on the results of some of these experiments.... ..."

### Table 3: Representations of massive fundamental monopoles and their threshold bound states. The notation for representations follows that of Tables 1 and 2.

1996

"... In PAGE 37: ... Other symmetry breaking patterns can be studied in a similar fashion. In Table3 we list the breakings of simple groups such that the unbroken group is a product of a simple group times a... In PAGE 38: ... These examples can in most cases be embedded in larger groups, in which case there will also be purely abelian fundamental monopoles and additional bound states containing these. In principle, all the bound states listed in Table3 must be realized as harmonic forms on appropriate moduli spaces. However, actually nding these forms is a rather nontrivial problem.... ..."

Cited by 1

### Table 1: E cient qsm algorithms for several fundamental problems. appears to make the qsm model more powerful than real parallel machines, since bandwidth limitations would normally dictate that there should be a gap parameter at memory as well as at processor (the two gap parameters need not necessarily be the same). The model considers contention only at individual memory locations, not at memory modules. In most machines, memory locations are organized in memory banks and access to each bank is queuing. Here again it appears that there is a mis-match between the qsm model and real machines. Both of the features of the qsm highlighted above give more power to the qsm than would appear to be warranted by current technology. However, in Section 4 we show that we can obtain a work-preserving emulation of the qsm on the bsp with only a modest slowdown. Since the bsp is considered to be a fairly good model of current parallel machines, this is a validation of the qsm as a general-purpose parallel computation model. It is also established in Section 4 that there is not much loss in generality in having the gap parameter only at processors, and not at memory locations.

"... In PAGE 5: ... It is also established in Section 4 that there is not much loss in generality in having the gap parameter only at processors, and not at memory locations. 3 Algorithmic Results Table1 summarizes the time and work bounds for qsm algorithms for several basic problems. Most of these results are the consequence of the following four Observations, all of which are from [22].... ..."

### Table 2: Refining the regions found by program LCP. LCP mavs

2002

"... In PAGE 23: ...7. Table2 summarizes the empirical results. LCP found six interesting GC- rich regions.... In PAGE 23: ...943. Table2 presents more examples of such refinements. 6 Concluding Remarks In this paper, two fundamental problems concerning the search for the heaviest segment of a sequence with length constraints are considered.... ..."

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### Table 1 Algorithms for DPS recognition.

2004

"... In PAGE 30: ...2 DPS Recognition and Digital Surface Segmentation DPS recognition and digital surface segmentation are fundamental problems in image analysis. Table1 lists di erent algorithms and their computational costs. All complexity bounds are given with respect to the number n of grid points in S.... ..."

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