We consider the problem of finding a shortest cycle (freely) homotopic to a given simple cycle on a compact, orientable surface. For this purpose, we use a pants decomposition of...
The planarization method has proven to be successful in graph drawing. The output, a combinatorial planar embedding of the so-called planarized graph, can be combined with state-o...
Let A be a d by n matrix, d < n. Let C be the regular cross polytope (octahedron) in Rn . It has recently been shown that properties of the centrosymmetric polytope P = AC are ...
We prove an upper bound, tight up to a factor of 2, for the number of vertices of level at most in an arrangement of n halfspaces in Rd , for arbitrary n and d (in particular, the...
Tracking the movement of people in indoor environments is useful for a variety of applications including elderly care, study of shopper behavior in shopping centers, security etc. ...