Faster Approximate Diameter and Distance Oracles in Planar Graphs

نویسندگان
چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Faster Approximate Diameter and Distance Oracles in Planar Graphs

We present an algorithm that computes a (1 + ε)-approximation of the diameter of a weighted, undirected planar graph of n vertices with non-negative edge lengths inO ( n logn ( logn+ (1/ε)5 )) expected time, improving upon the O ( n ( (1/ε)4 log4 n+ 2O(1/ε) )) -time algorithm of Weimann and Yuster [ICALP 2013]. Our algorithm makes two improvements over that result: first and foremost, it replac...

متن کامل

Faster Approximate Diameter and Distance

8 We present an algorithm that computes a (1 + ε)-approximation of the diameter of a weighted, 9 undirected planar graph of n vertices with non-negative edge lengths inO ( n logn ( logn+ (1/ε)5 )) 10 expected time, improving upon the O ( n ( (1/ε)4 log4 n+ 2O(1/ε) )) -time algorithm of Weimann 11 and Yuster [ICALP 2013]. Our algorithm makes two improvements over that result: first and 12 foremo...

متن کامل

Exact distance oracles for planar graphs

We present new and improved data structures that answer exact node-to-node distance queries in planar graphs. Such data structures are also known as distance oracles. For any directed planar graph on n nodes with non-negative lengths we obtain the following: • Given a desired space allocation S ∈ [n lg lgn, n], we show how to construct in Õ(S) time a data structure of size O(S) that answers dis...

متن کامل

Fast and Compact Oracles for Approximate Distances in Planar Graphs

We present an experimental evaluation of an approximate distance oracle recently suggested by Thorup [1] for undirected planar graphs. The oracle uses the existence of graph separators for planar graphs, discovered by Lipton and Tarjan [2], in order to divide the graph into smaller subgraphs. For a planar graph with n nodes, the algorithmic variant considered uses O(n(log n)/ ) preprocessing ti...

متن کامل

Faster Separators for Shallow Minor-Free Graphs via Dynamic Approximate Distance Oracles

Plotkin, Rao, and Smith (SODA’97) showed that any graph with m edges and n vertices that excludes Kh as a depth O(l logn)-minor has a separator of size O(n/l + lh logn) and that such a separator can be found in O(mn/l) time. A time bound of O(m + n/l) for any constant ǫ > 0 was later given (W., FOCS’11) which is an improvement for non-sparse graphs. We give three new algorithms. The first has t...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Algorithmica

سال: 2019

ISSN: 0178-4617,1432-0541

DOI: 10.1007/s00453-019-00570-z