Foreword
Discrete Comput Geom
Jacob E. Goodman · János Pach · Richard Pollack
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This special issue of Discrete & Computational Geometry commemorates two events
that took place during 2006. The first was the twentieth anniversary of the journal,
whose first issue appeared in January, 1986, and the second was the AMS-IMS-SIAM
Joint Summer Research Conference that took place during June, 2006 in Snowbird,
Utah, under the title “Discrete and Computational Geometry—Twenty Years Later.”
These events, of course, were not unrelated. In the summer of 1986, as a means of
calling attention to the new journal, the first and third of its present editors organized
a Joint Summer Research Conference in Santa Cruz, to which we invited outstanding
researchers in the areas of discrete geometry and computational geometry (as well
as a number of young people, including the second of DCG’s current editors), with
the aim of encouraging communication between the two fields, which we thought
would benefit each, and in fact of fostering collaboration between researchers in the
two areas. Discrete geometry, an old branch of mathematics that had flowered in
the late nineteenth and early twentieth centuries, had settled down to a steady flow
of results on polytopes, packings, geometry of numbers, and arrangements, spurred
mostly by the efforts of a few people (among them Hadwiger, Delone, Fejes Tóth,
Erdo˝s, Rogers, Cassels, Lekkerkerker, Klee, and Grünbaum), while computational
geometry was a brand new field that had only begun to emerge in the 1970s and 80s.
As can be judged by the explosion of work that followed in the next two decades,
and by the (now) frequent collaboration among researchers in both areas, our hopes
were realized. The journal itself burgeoned (from its original 400 pages a year to
its current 1440), two additional journals were started to cover the field of
computational geometry, numerous conferences were organized all over the world, and more
and more young researchers now list their primary area of interest as “discrete and
computational geometry.” Not only has the field itself grown immensely, but as it
has, surprising connections with other branches of mathematics and computer
science have opened up, to the mutual enrichment of both.
It has given us immense pleasure to help spur this development to its present peak
of activity, and we dedicate the present issue of DCG, which, as the reader will see,
covers a wide swath of mathematics and theoretical computer science, to the large
body of researchers who have taken part in the development of the field during the
past two decades; many of them are represented in its pages. (...truncated)