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.

Sharp Separation and Applications to Exact and Parameterized Algorithms

Abstract: Many divide-and-conquer algorithms employ the fact that the vertex set of a graph of bounded treewidth can be separated in two roughly balanced subsets by removing a small subset of vertices, referred to as a separator. In this paper we prove a trade-off between the size of the separator and the sharpness with which we can fix the size of the two sides of the partition. Our result appears to be a handy and powerful tool for the design of exact and parameterized algorithms for NP-hard problems. We illustrate that by presenting two applications. Our first application is a O(2 n+o(n))-time algorithm for the Degree Constrained Spanning Tree problem: find a spanning tree of a graph with the maximum number of nodes satisfying given degree constraints. This problem generalizes some well-studied problems, among them Hamiltonian Path, Full Degree Spanning Tree, Bounded Degree Spanning Tree, and Maximum Internal Spanning Tree. The second application is a parameterized algorithm with running time O(16 k+o(k)+n O(1)) for the k-Internal Out-Branching problem: here the goal is to compute an out-branching of a digraph with at least k internal nodes. This is a significant improvement over the best previously known parameterized algorithm for the problem by Cohen et al. (J. Comput. Syst. Sci. 76:650–662, 2010), running in time O(49.4k +n O(1)).

Spanning tree based state encoding for low power dissipation

Abstract: In this paper we address the problem of state encoding for synchronous finite state machines The primary goal is the reduction of switching activity in the state register At the beginning the state transition graph is transformed into an undirected graph where the edges are labeled with the state transition probabilities Next a maximum spanning tree of the undirected graph is constructed and we formulate the state encoding problem as an embedding of the spanning tree into a Boolean hypercube of unknown dimension At this point a modification of Prim's maximum spanning tree algorithm is presented to limit the dimension of the hypercube for area constraints Then we propose a polynomial time embedding heuristic, which removes the restriction of previous works, where the number of state bits used for encoding of a k-state FSM was generally limited to [log/sub 2/ k] Next a more sophisticated embedding algorithm is presented, which takes into account the state transition probabilities not covered by the spanning tree The resulting encodings of both algorithms often exhibit a lower switching activity and power dissipation in comparison with a known heuristic for low power state encoding

An empirical analysis of algorithms for constructing a minimum spanning tree

Abstract: We compare algorithms for the construction of a minimum spanning tree through largescale experimentation on randomly generated graphs of different structures and different densities In order to extrapolate with confidence, we use graphs with up to 130,000 nodes (sparse) or 750,000 edges (dense) Algorithms included in our experiments are Prim's algorithm (implemented with a variety of priority queues), Kruskal's algorithm (using presorting or demand sorting), Cheriton and Tarjan's algorithm, and Fredman and Tarjan's algorithm We also ran a large variety of tests to investigate low-level implementation decisions for the data structures, as well as to enable us to eliminate the effect of compilers and architectures

FPT algorithms for Connected Feedback Vertex Set

Abstract: We study the recently introduced Connected Feedback Vertex Set (CFVS) problem from the view-point of parameterized algorithms. CFVS is the connected variant of the classical Feedback Vertex Set problem and is defined as follows: given a graph G=(V,E) and an integer k, decide whether there exists F?V, |F|?k, such that G[V?F] is a forest and G[F] is connected. We show that Connected Feedback Vertex Set can be solved in time O(2 O(k) n O(1)) on general graphs and in time $O(2^{O(\sqrt{k}\log k)}n^{O(1)})$ on graphs excluding a fixed graph H as a minor. Our result on general undirected graphs uses, as a subroutine, a parameterized algorithm for Group Steiner Tree, a well studied variant of Steiner Tree. We find the algorithm for Group Steiner Tree of independent interest and believe that it could be useful for obtaining parameterized algorithms for other connectivity problems.