2 Open Problems from CCCG 2002

2 00 2 Open Problems from CCCG 2002

Is every zonohedron 3-colorable when viewed as a planar map? This question arose out of work described in [RSW01]. An equivalent question, under a different guise, is posed in [FHNS00]: Is the arrangement graph of great circles on the sphere 3colorable? Assume no three circles meet at a point, so that this graph is 4-regular. Circle graphs in the plane can require four colors [Koe90], so the ke...

Open Problems from CCCG 2002

Is every zonohedron 3-colorable when viewed as a planar map? This question arose out of work described in [RSW01]. An equivalent question, under a different guise, is posed in [FHNS00]: Is the arrangement graph of great circles on the sphere 3colorable? Assume no three circles meet at a point, so that this graph is 4-regular. Circle graphs in the plane can require four colors [Koe90], so the ke...

1-bend 3-D orthogonal drawings: two open problems solved

Open Problems: Open Problems from CCCG 2005

Consider the following special case of planar point location: preprocess k sets of lines, where each set consists of parallel lines, to support queries of the form “given a point p, what is the line immediately above or below p?” What is the fastest possible query time as a function of k and the total number n of lines? In other words, the n given lines have k distinct orientations. See Figure ...

Open Problems from CCCG 2015

The following is a description of the problems pre-Is it possible to find the largest-area bounded cell in an arrangement of n lines in R 2 (Figure 1) in subquadratic time? Sariel Har-Peled observed that α Figure 1: An arrangement and its largest cell area α. if the largest cell's area α is much greater than its expected area 1/n 2 , then random sampling permits achieving expected subquadratic ...