### Table 2.2: Rectilinear Crossing Numbers up to n = 17

2006

Cited by 1

### Table 10: Di cult rectilinear instances. See text for instance descriptions and

2000

"... In PAGE 23: ... Zachariasen [27] noted that the rectilinear FST generator actually produced a super-polynomial number of FSTs for this series of instances. In Table10 we present statistics on the rst ve instances in this series (12-52 ter- minals). The number of FSTs and the total CPU-time grows rapidly although the structure of the optimal solutions (number of FSTs and average size) does not di er radically from randomly generated instances.... ..."

Cited by 33

### Table 1: Time needed for L1-, rectilinear link distance, and smallest path queries.

1996

"... In PAGE 2: ...ength. His data structure needs O(n log n) space and preprocessing. We summarize the results in the following table (k is used to denote the link length of the shortest path). In this paper we present a data structure that achieves the same time complexities as shown in Table1 but improves both the space and prepro- cessing requirements to linear in the number of vertices of the polygon.... ..."

Cited by 5

### Table 1: Complexity of rectilinear trees.

"... In PAGE 1: ... However, it is still a major open problem in VLSI whether the RSA problem can be solved in polynomial time. For completeness, previous results on the complex- ity of rectilinear trees are listed in Table1 . More infor- mation can be found in the book by Hwang, Richards and Winter [9].... ..."

### Table 6.1: Experimental Results B4CZ BPBDBHB5.

2001

Cited by 6

### Table 1. The in uence of full components in B amp; B and dyn. prog. In the next section we review some basics on rectilinear Steiner tree problems, we derive new properties for full components which could be part of the SMT. Further we give statistics for the enormous pro t we gain. In Section 3 we propose an alternative way to put the components together such that many subsets do not need to be considered and give theoretical bounds as well as practical results for this approach. Finally, we demonstrate the implementation of our approaches giving the results of about one thousand experiments. Following a tradition of [5,14] to show a Steiner minimum tree of relatively big size on page 2 of the paper, we display in Fig. 1 an SMT with 100 terminals. The theoretical results used in this paper will be summarized in the poster session of [4].

1997

"... In PAGE 3: ... prog. To demonstrate the enormous importance of the number of full components for both the dynamic programming and the Branch amp; Bound approach we give two concrete examples in Table1 (with 20 resp. 31 terminals).... ..."

Cited by 12

### Table II. Effect of measurement noise on estimated parameters. Simulated data, Model I.

1998

### Table 1: asymptotics for Ca(n) compared with known bounds 5

2000

"... In PAGE 6: ...Ca(n) = a Ca(k) + a2 !k f(k) + 2a a?1 2 2 !e(k; k; k) + a2 !i(k; k) + cr(Ka) k4 : (10) We can solve for a non-recursive closed form of Ca(n) by simplifying na cr(Ka) + loga n?1 X j=1 aj?1 quot; a 2 !k f(k) + a 2 !i(k; k) + 2a a?1 2 2 !e(k; k; k) + cr(Ka) k4# ; (11) where k = n=aj. Out of all recursive constructions for which cr(Ka) is known, the best results are achieved by C3(n) (see Table1 ). The construction can easily be generalized by dividing n into three parts of sizes bn3 c, dn3e, and n?bn3 c?dn3 e.... In PAGE 11: ... Our third and nal open question concerns a problem addressed by Hayward [Hay87] and Newborn and Moser [NM80] and is the following: nd a rectilinear embedding of Kn that produces the largest number of simple n-gons. Hayward, building on the work in [NM80] has asymptotics based on a generalized rectilinear embedding of Kn, as mentioned in Section 3, Table1 . Our construction given in Section 3 improves Hawyard apos;s result [BDG00].... ..."

Cited by 3

### Table 2: The number of routing tracks created for each application by each routing generation algorithm. Lower bounds are based on the original unroutable signal cross-sections of the placements.

"... In PAGE 8: ... 4.2 Track Count Analysis Table2 lists the number of routing tracks created by each flexible routing generation algorithm for each application, along with lower bounds represented by the UCS values of the original placements before routing generation. These bounds are most likely infeasible due to the large number of bus connectors required for the increased wire sharing between signals from different netlists.... In PAGE 8: ... This issue could lead to the creation of more tracks than necessary. AMO generally results in architectures with fewer tracks but more bus connectors than AML, as demonstrated by correlating the results in Table2 with those in Figure 10. This is logical, as AML places a greater emphasis on local track creation, but may create more overall tracks as a result.... ..."