The Minimum Feasible Tileset Problem
نویسندگان
چکیده
We consider the Minimum Feasible Tileset problem: Given a set of symbols and subsets of these symbols (scenarios), find a smallest possible number of pairs of symbols (tiles) such that each scenario can be formed by selecting at most one symbol from each tile. We show that this problem is NP-complete even if each scenario contains at most three symbols. Our main result is a 4/3-approximation algorithm for the general case. In addition, we show that the Minimum Feasible Tileset problem is fixed-parameter tractable both when parameterized with the number of scenarios and with the number of symbols.
منابع مشابه
Inverse feasible problem
In many infeasible linear programs it is important to construct it to a feasible problem with a minimum pa-rameters changing corresponding to a given nonnegative vector. This paper defines a new inverse problem, called “inverse feasible problem”. For a given infeasible polyhedron and an n-vector a minimum perturba-tion on the parameters can be applied and then a feasible polyhedron is concluded.
متن کاملThe periodic domino problem revisited
In this article we give a new proof of the undecidability of the periodic domino problem. The main difference with the previous proofs is that this one does not start from a proof of the undecidability of the (general) domino problem but only from the existence of an aperiodic tileset. The formalism of Wang tiles was introduced in [Wan61] to study decision procedures for the ∀∃∀ fragment of the...
متن کاملCapacity Inverse Minimum Cost Flow Problem under the Weighted Hamming Distances
Given an instance of the minimum cost flow problem, a version of the corresponding inverse problem, called the capacity inverse problem, is to modify the upper and lower bounds on arc flows as little as possible so that a given feasible flow becomes optimal to the modified minimum cost flow problem. The modifications can be measured by different distances. In this article, we consider the capac...
متن کاملDilatation of self-assembling tilings
We introduce a new notion in self-assembly, that of transforming the dynamics of assembly. This notion allows us to have transformation of the plane computed within the assembly process. More specifically, we study a zooming transformation. First we show that the possibility of doing that transformation depends on the regularity of the assembly process, as expressed by the order condition. Then...
متن کاملA mathematical model for the multi-mode resource investment problem
This paper presents an exact model for the resource investment problem with generalized precedence relations in which the minimum or maximum time lags between a pair of activities may vary depending on the chosen modes. All resources considered are renewable. The objective is to determine a mode and a start time for each activity so that all constraints are obeyed and the resource investment co...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014