We show that finding orthogonal grid-embeddings of plane graphs (planar with fixed combinatorial embedding) with the minimum number of bends in the so-called Kandinsky model (which allows vertices of degree > 4) is NP-complete, thus solving a long-standing open problem. On the positive side, we give an efficient algorithm for several restricted variants, such as graphs of bounded branch width a...

A 1.5D terrain is an x-monotone polyline with n vertices. An imprecise 1.5D terrain is a 1.5D terrain with a y-interval at each vertex, rather than a fixed y-coordinate. A realization of an imprecise terrain is a sequence of n y-coordinates—one for each interval— such that each y-coordinate is within its corresponding interval. For certain applications in terrain analysis, it is important to be...

L.A. Shepp has posed aild analyzed the problem of optimal random drawinp with Jut replacement from an urn containing predetermined numbers of plus and minus balls. ;Here Shepp’s results are extended by improving the bounds on value; of penturbeu urns, deriving an exact algorithm for the urn values and computing the stopping boundary for urns of u-, tn 200 balls.

A k-uniform, d-regular instance of Exact Cover is a family of m sets Fn,d,k = {Sj ⊆ {1, . . . , n}}, where each subset has size k and each 1 ≤ i ≤ n is contained in d of the Sj . It is satisfiable if there is a subset T ⊆ {1, . . . , n} such that |T ∩ Sj | = 1 for all j. Alternately, we can consider it a d-regular instance of Positive 1-in-k SAT, i.e., a Boolean formula with m clauses and n var...

The Dial-A-Ride Problem (DARP) has often been used to organize transport of elderly and handicapped people, assuming that these people can book their transport in advance. But the DARP can also be used to organize usual passenger or goods transportation in real online scenarios with time window constraints. This paper presents an efficient exact algorithm with significantly reduced calculation ...

Finding common motifs from a set of strings coding biological sequences is an important problem in Molecular Biology. Several versions of the motif finding problem have been proposed in the literature and for each version, numerous algorithms have been developed. However, many of these algorithms fall under the category of heuristics. In this paper, we concentrate on the Simple Motif Problem (S...

Given a set of rectangular items of different sizes and a rectangular container, the aim of the bi-dimensional Orthogonal Packing Problem (OPP-2 for short) is to decide whether there exists a non-overlapping packing of the items in this container. The rotation of items is not allowed. In this paper we present a new exact algorithm for solving OPP-2, based upon the characterization of solutions ...