Consider the following one-player game. Take a well-formed sequence of opening and closing brackets (a Dyck word). As a move, the player can pair any opening bracket with any closing bracket to its right, erasing them. The goal is to re-pair (erase) the entire sequence, and the cost of a strategy is measured by its width: the maximum number of nonempty segments of symbols (separated by blank space) seen during the play.

Article Free Access Share on Construction of contour trees in 3D in O(n log n) steps Authors: Sergey P. Tarasov Computing Center of RAS, Vavilova 40, 117967 Moscow GSP-1, Russia Computing Center of RAS, Vavilova 40, 117967 Moscow GSP-1, RussiaView Profile , Michael N. Vyalyi Computing Center of RAS, Vavilova 40, 117967 Moscow GSP-1, Russia Computing Center of RAS, Vavilova 40, 117967 Moscow GSP-1, RussiaView Profile Authors Info & Claims SCG '98: Proceedings of the fourteenth annual symposium on Computational geometryJune 1998 Pages 68–75https://doi.org/10.1145/276884.276892Published:07 June 1998Publication History 57citation703DownloadsMetricsTotal Citations57Total Downloads703Last 12 Months34Last 6 weeks10 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

We find some obstructions for piecewise-linear (PL) functions defined on two-dimensional closed compact manifolds (surfaces) to be heightfunctionsin R3 andprove existenceof some non-height PL tiutctions.On the other hand we prove thatall PL functions on a sphereare heightfunctions.