GRAPH EMBEDDINGS 1988: Recent Breakthroughs, New Directions

THE PAST FEW YEARS HAVE SEEN A NUMBER OF RESULTS ON GRAPH EMBEDDINGS THAT DESERVE TO BE CALLED `BREAKTHROUGHS'' BECAUSE OF THEIR SETTLING HARD OPEN PROBLEMS AND/OR THEIR RAISING IMPORTANT ISSUES THAT PROMISE TO ALTER THE DIRECTION OF SUBSEQUENT RESEARCH ON GRAPH EMBEDDINGS. WE DESCRIBE AND DISCUSS SEVERAL SUCH RESULTS.

[1]  Paul C. Kainen,et al.  The book thickness of a graph , 1979, J. Comb. Theory, Ser. B.

[2]  Joel Friedman,et al.  Expanding graphs contain all small trees , 1987, Comb..

[3]  Susanne E. Hambrusch,et al.  Embedding large tree machines into small ones , 1988 .

[4]  Lenwood S. Heath,et al.  The page number of genus g graphs is (g) , 1987, STOC.

[5]  Abbas El Gamal,et al.  Configuration of VLSI Arrays in the Presence of Defects , 1984, JACM.

[6]  Arnold L. Rosenberg,et al.  Optimal simulations of tree machines , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[7]  Arnold L. Rosenberg,et al.  Optimal simulations by Butterfly Networks , 1988, STOC '88.

[8]  Mihalis Yannakakis,et al.  Four pages are necessary and sufficient for planar graphs , 1986, Symposium on the Theory of Computing.

[9]  Arnold L. Rosenberg,et al.  Cost Trade-offs in Graph Embeddings, with Applications , 1983, JACM.

[10]  Frank Thomson Leighton,et al.  Wafer-Scale Integration of Systolic Arrays , 1985, IEEE Trans. Computers.

[11]  Frank Thomson Leighton,et al.  Reconfiguring a hypercube in the presence of faults , 1987, STOC.

[12]  Lenwood S. Heath Embedding outerplanar graphs in small books , 1987 .

[13]  Franco P. Preparata,et al.  The cube-connected-cycles: A versatile network for parallel computation , 1979, 20th Annual Symposium on Foundations of Computer Science (sfcs 1979).

[14]  Jin-Yi Cai,et al.  Take a walk, grow a tree , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[15]  Arnold L. Rosenberg,et al.  The physical mapping problem for parallel architectures , 1988, JACM.

[16]  Arnold L. Rosenberg,et al.  The Diogenes Approach to Testable Fault-Tolerant Arrays of Processors , 1983, IEEE Transactions on Computers.

[17]  Arnold L. Rosenberg,et al.  Embedding graphs in books: a layout problem with applications to VLSI design , 1985 .