On the Complexity of Submap Isomorphism
نویسندگان
چکیده
Generalized maps describe the subdivision of objects in cells, and incidence and adjacency relations between cells, and they are widely used to model 2D and 3D images. Recently, we have defined submap isomorphism, which involves deciding if a copy of a pattern map may be found in a target map, and we have described a polynomial time algorithm for solving this problem when the pattern map is connected. In this paper, we show that submap isomorphism becomes NP-complete when the pattern map is not connected, by reducing the NP-complete problem Planar-4 3-SAT to it.
منابع مشابه
On the complexity of submap isomorphism and maximum common submap problems
Generalized maps describe the subdivision of objects in cells and are widely used to model 2D and 3D images. In this context, several pattern recognition tasks involve solving submap isomorphism problems (to decide if a map is included in another map) or, more generally, computing maximum common submaps (to measure the distance between two maps). Recently, we have described a polynomial-time al...
متن کاملA Polynomial Algorithm for Submap Isomorphism: Application to Searching Patterns in Images
In this paper, we address the problem of searching for a pattern in a plane graph, i.e., a planar drawing of a planar graph. To do that, we propose to model plane graphs with 2-dimensional combinatorial maps, which provide nice data structures for modelling the topology of a subdivision of a plane into nodes, edges and faces. We define submap isomorphism, we give a polynomial algorithm for this...
متن کاملTowards Multi-Vehicle Simultaneous Localisation and Mapping
This paper presents a novel approach to the multi-vehicle Simultaneous Localisation and Mapping (SLAM) problem that exploits the manner in which observations are fused into the global map of the environment to manage the computational complexity of the algorithm and improve the data association process. Rather than incorporating every observation directly into the global map of the environment,...
متن کاملAn Efficient Approach to the Simultaneous Localisation and Mapping Problem
This paper presents a novel approach to the Simultaneous Localisation and Mapping (SLAM) algorithm that exploits the manner in which observations are fused into the global map of the environment to manage the computational complexity of the algorithm and improve the data association process. Rather than incorporating every observation directly into the global map of the environment, the Constra...
متن کاملPolynomial algorithms for subisomorphism of nD open combinatorial maps
Combinatorial maps describe the subdivision of objects in cells, and incidence and adjacency relations between cells, and they are widely used to model 2D and 3D images. However, there is no algorithm for comparing combinatorial maps, which is an important issue for image processing and analysis. In this paper, we address two basic comparison problems, i.e., map isomorphism, which involves deci...
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 2013