Planar graphs can be represented as the intersection of different types geometric objects in plane, e.g., circles (Koebe, 1936), line segments (Chalopin & Gonçalves, SODA 2009), L-shapes (Gonçalves et al., 2018). For general graphs, however, even deciding whether such representations exist is often NP-hard. We consider apex i.e., that made planar by removing one vertex from them. show, somewhat...

In this paper, an eecient algorithm to simultaneously implement array alignment and data/computation distribution is introduced and evaluated. We re-visit previous work of Li and Chen 13, 14], and we show that their alignment step should not be conducted without preserving the potential parallelism. In other words, the optimal alignment may well sequentialize computations, whatever the distribu...

assigning facilities to locations is one of the important problems, which significantly is influence in transportation cost reduction. in this study, we solve quadratic assignment problem (qap), using a meta-heuristic algorithm with deterministic tasks and equality in facilities and location number. it should be noted that any facility must be assign to only one location. in this paper, first o...

We prove that multilinear (tensor) analogues of many efficiently computable problems in numerical linear algebra are NP-hard. Our list here includes: determining the feasibility of a system of bilinear equations, deciding whether a 3-tensor possesses a given eigenvalue, singular value, or spectral norm; approximating an eigenvalue, eigenvector, singular vector, or the spectral norm; and determi...

The antibiotics time machine is an optimization question posed by Mira et al. on the design of antibiotic treatment plans to minimize antibiotic resistance. The problem is a variation of the Markov decision process. These authors asked if the problem can be solved efficiently. In this paper, we show that this problem is NP-hard in general. 1. Problem statement and results Resistance to antibiot...

Extensions of the ML type system based on con strained type schemes have been proposed for lan guages with overloading Type inference in these sys tems requires solving the following satis ability prob lem Given a set of type assumptions C over nite types and a type basis A is there is a substitution S that satis es C in that A CS is derivable Un der arbitrary overloading the problem is undecid...

We construct three public key knapsack cryptosystems. Standard knapsack cryptosystems hide easy instances of the knapsack problem and have been broken. The systems considered in the article face this problem: They hide a random (possibly hard) instance of the knapsack problem. We provide both complexity results (size of the key, time needed to encypher/decypher...) and experimental results. Sec...

Given a set M ⊂ Z, an enclosing polyhedron for M is any polyhedron P such that the set of integer points contained in P is precisely M . Representing a discrete volume by enclosing polyhedron is a fundamental problem in visualization. In this paper we propose the first proof of the long-standing conjecture that the problem of finding an enclosing polyhedron with a minimal number of 2-facets is ...

Discrete tomography deals with reconstructing finite spatial objects from their projections. The objects we study in this paper are called tilings or tile-packings, and they consist of a number of disjoint copies of a fixed tile, where a tile is defined as a connected set of grid points. A row projection specifies how many grid points are covered by tiles in a given row; column projections are ...