scholarly journals Fast Algorithms for Diameter-Optimally Augmenting Paths and Trees

2019 ◽  
Vol 30 (02) ◽  
pp. 293-313
Author(s):  
Ulrike Große ◽  
Christian Knauer ◽  
Fabian Stehn ◽  
Joachim Gudmundsson ◽  
Michiel Smid
Keyword(s):  
Metric Space ◽  
Fast Algorithms ◽  
Exact Algorithms ◽  
Input Graph ◽  
Additional Edge ◽  
Vertex Graph

We consider the problem of augmenting an [Formula: see text]-vertex graph embedded in a metric space, by inserting one additional edge in order to minimize the diameter of the resulting graph. We present exact algorithms for the cases when (i) the input graph is a path, running in [Formula: see text] time, and (ii) the input graph is a tree, running in [Formula: see text] time. We also present an algorithm for paths that computes a [Formula: see text]-approximation in [Formula: see text] time.

scholarly journals Time and space efficient quantum algorithms for detecting cycles and testing bipartiteness

2018 ◽  
Vol 18 (1&2) ◽  
pp. 18-50 ◽  
Author(s):  
Chris Cade ◽  
Ashley Montanaro ◽  
Aleksandrs Belovs
Keyword(s):  
Matrix Model ◽  
Adjacency Matrix ◽  
Maximum Degree ◽  
Quantum Algorithms ◽  
Input Graph ◽  
Time And Space ◽  
Quantum Bits ◽  
Graph Problems ◽  
Vertex Graph ◽  
Connectivity Problem

We study space and time-efficient quantum algorithms for two graph problems – deciding whether an n-vertex graph is a forest, and whether it is bipartite. Via a reduction to the s-t connectivity problem, we describe quantum algorithms for deciding both properties in O˜(n 3/2 ) time whilst using O(log n) classical and quantum bits of storage in the adjacency matrix model. We then present quantum algorithms for deciding the two properties in the adjacency array model, which run in time O˜(n √ dm) and also require O(log n) space, where dm is the maximum degree of any vertex in the input graph.

scholarly journals Finding hidden cliques in linear time

2010 ◽  
Vol DMTCS Proceedings vol. AM,... (Proceedings) ◽  
Author(s):  
Uriel Feige ◽  
Dorit Ron
Keyword(s):  
High Probability ◽  
Linear Time ◽  
Maximum Clique ◽  
Spectral Approach ◽  
Input Graph ◽  
Random Choice ◽  
Spectral Techniques ◽  
Vertex Graph ◽  
International Audience ◽  
Linear Time Algorithms

International audience In the hidden clique problem, one needs to find the maximum clique in an $n$-vertex graph that has a clique of size $k$ but is otherwise random. An algorithm of Alon, Krivelevich and Sudakov that is based on spectral techniques is known to solve this problem (with high probability over the random choice of input graph) when $k \geq c \sqrt{n}$ for a sufficiently large constant $c$. In this manuscript we present a new algorithm for finding hidden cliques. It too provably works when $k > c \sqrt{n}$ for a sufficiently large constant $c$. However, our algorithm has the advantage of being much simpler (no use of spectral techniques), running faster (linear time), and experiments show that the leading constant $c$ is smaller than in the spectral approach. We also present linear time algorithms that experimentally find even smaller hidden cliques, though it remains open whether any of these algorithms finds hidden cliques of size $o(\sqrt{n})$.

Recognition of Birds in Blurred and Illumination Images by Local Features

2017 ◽  
Vol 7 (7) ◽  
pp. 243
Author(s):  
Suresha .M ◽  
. Sandeep
Keyword(s):  
Computer Vision ◽  
Time Complexity ◽  
Feature Detection ◽  
Feature Matching ◽  
Fast Algorithms ◽  
Local Features ◽  
Experimental Demonstration ◽  
Harris Corner ◽  
Blurred Image ◽  
Blurred Images

Local features are of great importance in computer vision. It performs feature detection and feature matching are two important tasks. In this paper concentrates on the problem of recognition of birds using local features. Investigation summarizes the local features SURF, FAST and HARRIS against blurred and illumination images. FAST and Harris corner algorithm have given less accuracy for blurred images. The SURF algorithm gives best result for blurred image because its identify strongest local features and time complexity is less and experimental demonstration shows that SURF algorithm is robust for blurred images and the FAST algorithms is suitable for images with illumination.

On Asymmetric Distances

2013 ◽  
Vol 1 ◽  
pp. 200-231 ◽  
Author(s):  
Andrea C.G. Mennucci
Keyword(s):  
Total Variation ◽  
Calculus Of Variations ◽  
Distance Function ◽  
Metric Space ◽  
Metric Spaces ◽  
Geodesic Segment ◽  
Intrinsic Metric ◽  
Typical Application ◽  
Variation Formula

Abstract In this paper we discuss asymmetric length structures and asymmetric metric spaces. A length structure induces a (semi)distance function; by using the total variation formula, a (semi)distance function induces a length. In the first part we identify a topology in the set of paths that best describes when the above operations are idempotent. As a typical application, we consider the length of paths defined by a Finslerian functional in Calculus of Variations. In the second part we generalize the setting of General metric spaces of Busemann, and discuss the newly found aspects of the theory: we identify three interesting classes of paths, and compare them; we note that a geodesic segment (as defined by Busemann) is not necessarily continuous in our setting; hence we present three different notions of intrinsic metric space.

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