Prim's algorithm

About: Prim's algorithm is a research topic. Over the lifetime, 775 publications have been published within this topic receiving 17971 citations. The topic is also known as: DJP algorithm & Jarník algorithm.

A randomized linear-time algorithm to find minimum spanning trees

Abstract: We present a randomized linear-time algorithm to find a minimum spanning tree in a connected graph with edge weights. The algorithm uses random sampling in combination with a recently discovered linear-time algorithm for verifying a minimum spanning tree. Our computational model is a unit-cost random-access machine with the restriction that the only operations allowed on edge weights are binary comparisons.

A minimum spanning tree algorithm with inverse-Ackermann type complexity

Abstract: A deterministic algorithm for computing a minimum spanning tree of a connected graph is presented. Its running time is 0(m a(m, n)), where a is the classical functional inverse of Ackermann's function and n (respectively, m) is the number of vertices (respectively, edges). The algorithm is comparison-based : it uses pointers, not arrays, and it makes no numeric assumptions on the edge costs.

Prime Object Proposals with Randomized Prim's Algorithm

Abstract: Generic object detection is the challenging task of proposing windows that localize all the objects in an image, regardless of their classes. Such detectors have recently been shown to benefit many applications such as speeding-up class-specific object detection, weakly supervised learning of object detectors and object discovery. In this paper, we introduce a novel and very efficient method for generic object detection based on a randomized version of Prim's algorithm. Using the connectivity graph of an image's super pixels, with weights modelling the probability that neighbouring super pixels belong to the same object, the algorithm generates random partial spanning trees with large expected sum of edge weights. Object localizations are proposed as bounding-boxes of those partial trees. Our method has several benefits compared to the state-of-the-art. Thanks to the efficiency of Prim's algorithm, it samples proposals very quickly: 1000 proposals are obtained in about 0.7s. With proposals bound to super pixel boundaries yet diversified by randomization, it yields very high detection rates and windows that tightly fit objects. In extensive experiments on the challenging PASCAL VOC 2007 and 2012 and SUN2012 benchmark datasets, we show that our method improves over state-of-the-art competitors for a wide range of evaluation scenarios.

A local clustering algorithm for massive graphs and its application to nearly linear time graph partitioning

Abstract: We study the design of local algorithms for massive graphs A local graph algorithm is one that finds a solution containing or near a given vertex without looking at the whole graph We present a local clustering algorithm Our algorithm finds a good cluster---a subset of vertices whose internal connections are significantly richer than its external connections---near a given vertex The running time of our algorithm, when it finds a nonempty local cluster, is nearly linear in the size of the cluster it outputs The running time of our algorithm also depends polylogarithmically on the size of the graph and polynomially on the conductance of the cluster it produces Our clustering algorithm could be a useful primitive for handling massive graphs, such as social networks and web-graphs As an application of this clustering algorithm, we present a partitioning algorithm that finds an approximate sparsest cut with nearly optimal balance Our algorithm takes time nearly linear in the number edges of the graph