External Data Structures for Shortest Path Queries on Planar Digraphs
نویسندگان
چکیده
In this paper we present space-query trade-offs for external memory data structures that answer shortest path queries on planar directed graphs. For any S = Ω(N ) and S = O(N/B), our main result is a family of structures that use S space and answer queries in O( 2 SB ) I/Os, thus obtaining optimal space-query product O(N/B). An S space structure can be constructed in O( √ S · sort(N)) I/Os, where sort(N) is the number of I/Os needed to sort N elements, B is the disk block size, and N is the size of the graph.
منابع مشابه
Eecient Algorithms for Shortest Path Queries in Planar Digraphs ?
This paper describes algorithms for answering shortest path queries in digraphs with small separators and, in particular, in planar digraphs. In this version of the problem, one has to preprocess the input graph so that, given an arbitrary pair of query vertices v and w, the shortest-path distance between v and w can be computed in a short time. The goal is to achieve balance between the prepro...
متن کاملAn External Memory Data Structure for Shortest Path Queries ( Extended Abstract ) ⋆
We present results related to satisfying shortest path queries on a planar graph stored in external memory. In particular, we show how to store rooted trees in external memory so that bottom-up paths can be traversed I/O-efficiently, and we present I/O-efficient algorithms for triangulating planar graphs and computing small separators of such graphs. Using these techniques, we can construct a d...
متن کاملAn External - Memory Data Structure for Shortest Path
In this paper, we present results related to satisfying shortest path queries on a planar graph stored in external memory. N denotes the total number of vertices and edges in the graph and sort(N) denotes the number of input/output (I/O) operations required to sort an array of length N. 1) We describe a data structure for supporting bottom-up traversal of rooted trees in external memory. A tree...
متن کاملExact Shortest Path Queries for Planar Graphs Using Linear Space
We provide the first linear-space data structure with provable sublinear query time for exact point-topoint shortest path queries in planar graphs. We prove that for any planar graph G with non-negative arc lengths and for any > 0 there is a data structure that supports exact shortest path and distance queries in G with the following properties: the data structure can be created in time O(n lg(...
متن کاملFast Algorithms for Maintaining Shortest Paths in Outerplanar and Planar Digraphs
We present algorithms for maintaining shortest path information in dynamic outerplanar digraphs with sublogarithmic query time. By choosing appropriate parameters we achieve continuous trade-offs between the preprocessing, query, and update times. Our data structure is based on a recursive separator decomposition of the graph and it encodes the shortest paths between the members of a properly c...
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 2005