Open problems from cccg 2001

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 2008

A swimmer falls overboard in an equilateral triangle lake in a fog. If the edge length of the triangle is 1, what is the shortest length swimming path that ensures the swimmer will reach the shore? Swimming one unit straight in any direction certainly reaches the shore. The problem was originally posed in 1963. Besicovitch showed shortly afterward that a 3-link chain of length 3 √ 21/14 = 0.981...

Open Problems from CCCG 2006

An edge reconnection is an operation on a path of three consecutive vertices (a, b, c) of a chain or tree linkage; refer to Figure 1. If it is possible to fold the linkage, preserving edge lengths and avoiding self-intersection, to bring the two incident edges ab and bc into coincidence, then the edge reconnection breaks the connection between the edges at b, splits b into two vertices b1 and b...

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 ...