### Table 2: Review of NP-completeness results for graph layout problems.

2002

"... In PAGE 6: ... It is possible to show that many layout problems remain NP-complete even for cer- tain restricted classes of graphs. Table2 summarizes these known negative results and also includes references for the proofs of Theorem 1. Fixed parameter results.... ..."

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### Table 2: The complexity of the colouring of circle graphs 6 Conclusions We presented in this article a nearly complete description of the complexity of the colouring problems of circle graph. Table 2 shows this in a compact version. There are two problems still open. One is a minor one: How many levels must a circle graph have, such that the colouring problem is NP-complete? The second open problem is the complexity of the colouring problem for g-segment graphs. Acknowledgment Many discussions with B. Monien accompanied this work. His help is gratefully acknowledged.

### Table 1. Summary of results. NPCmeans that the problem is NP-complete.

1997

"... In PAGE 3: ... Since we can prove that it is NP-complete to decide whether a 2-connected planar graph of maximum degree 2 T ? 1 has a T -spanning tree, this result establishes a complete characterization of the T -spanning tree problem for k-connected planar graphs of maximum degree G. Table1 summarizes the results (it assumes that G gt; T 2). Organization of the paper Section 2 provides basic terminology.... ..."

Cited by 5

### Table 1. Summary of results. NPCmeans that the problem is NP-complete.

1997

"... In PAGE 3: ... Since we can prove that it is NP-complete to decide whether a 2-connected planar graph of maximum degree 2 T ? 1 has a T -spanning tree, this result establishes a complete characterization of the T -spanning tree problem for k-connected planar graphs of maximum degree G. Table1 summarizes the results (it assumes that G gt; T 2). Organization of the paper Section 2 provides basic terminology.... ..."

Cited by 5

### Table 1. Summary of results. NPCmeans that the problem is NP-complete.

1997

"... In PAGE 3: ... Since we can prove that it is NP-complete to decide whether a 2-connected planar graph of maximum degree 2 T ? 1 has a T -spanning tree, this result establishes a complete characterization of the T -spanning tree problem for k-connected planar graphs of maximum degree G. Table1 summarizes the results (it assumes that G gt; T 2). Organization of the paper Section 2 provides basic terminology.... ..."

Cited by 5

### Table 2: Complexity of AHNEPs solving NP-complete problems

### Table 2: Possible Multiobjective NP-Complete Functions NP-Complete Problem Examples

"... In PAGE 4: ... This may prevent general comparison between various MOEAs, but the problems apos; inherent di culty should present the desired algorithmic challenges and complement numeric test suite MOPs. Table2 suggests possible NP- Complete MOPs for inclusion. To date, only two non-nu- merical MOP examples are found in the MOEA literature: one is a multiobjective NP-Complete example (a multiob- 0 0.... ..."

### Table 1: The complexity of FCSPs Problem Restriction Sequential Complexity Parallel Complexity FCSP decision binary relations NP-complete

"... In PAGE 5: ... In addition to the theoretical results, we have simulated the ne-grain distributed algorithm based on logical time assumptions and experimented with the coarse-grain distributed algo- rithm on a network of transputers. Table1 summarizes current knowledge on the complexity of FCSPs; our results are marked with (y). The rest of the paper is organized as follows.... ..."

### Table 1: Comparison of sum of cluster densities for MDS Peeling+DPRP and for the best of 10 Density-FM runs. Results for avq.small benchmark using Density-FM would require many days of SPARC-10 time. Bounded Size Maximum Density Subhyper- graph (BMDS) problem : Given a hypergraph H(V; E) and an integer B, nd the subhypergraph of H with maximum density and size B. While MDS was polynomial time solvable, BMDS is shown NP-complete by reduction from Maxi- mum Clique.

1995

"... In PAGE 2: ... Our FM variant, which we call Density-FM, is standard k-way FM with gains updated based on the sum of densities metric; our implementation adapts code from [13]. Table1 com- pares MDS Peeling+DPRP against the best result of 10 Density-FM runs. MDS Peeling+DPRP averages 5.... ..."

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