scholarly journals THE FIRST APPROXIMATED DISTRIBUTED ALGORITHM FOR THE MINIMUM DEGREE SPANNING TREE PROBLEM ON GENERAL GRAPHS

2004 ◽  
Vol 15 (03) ◽  
pp. 507-516 ◽  
Author(s):  
LÉLIA BLIN ◽  
FRANCK BUTELLE
Keyword(s):  
Distributed Algorithm ◽  
Spanning Tree ◽  
Time Complexity ◽  
Minimum Degree ◽  
Np Hard ◽  
Message Complexity ◽  
General Graphs

In this paper we present the first distributed algorithm on general graphs for the Minimum Degree Spanning Tree problem. The problem is NP-hard in sequential. Our algorithm give a Spanning Tree of a degree at most 1 from the optimal. The resulting distributed algorithm is asynchronous, it works for named asynchronous arbitrary networks and achieves O(|V|) time complexity and O(|V||E|) message complexity.

scholarly journals Synchronous Context-Free Grammars and Optimal Parsing Strategies

2016 ◽  
Vol 42 (2) ◽  
pp. 207-243
Author(s):  
Daniel Gildea ◽  
Giorgio Satta
Keyword(s):  
Approximation Algorithms ◽  
Time Complexity ◽  
Space Complexity ◽  
Sentence Length ◽  
Np Hard ◽  
Space And Time ◽  
Context Free ◽  
General Graphs ◽  
Context Free Grammars

The complexity of parsing with synchronous context-free grammars is polynomial in the sentence length for a fixed grammar, but the degree of the polynomial depends on the grammar. Specifically, the degree depends on the length of rules, the permutations represented by the rules, and the parsing strategy adopted to decompose the recognition of a rule into smaller steps. We address the problem of finding the best parsing strategy for a rule, in terms of space and time complexity. We show that it is NP-hard to find the binary strategy with the lowest space complexity. We also show that any algorithm for finding the strategy with the lowest time complexity would imply improved approximation algorithms for finding the treewidth of general graphs.

AN EFFICIENT DISTRIBUTED ALGORITHM FOR 3-EDGE-CONNECTIVITY

2006 ◽  
Vol 17 (03) ◽  
pp. 677-701 ◽  
Author(s):  
YUNG H. TSIN
Keyword(s):  
Distributed Algorithm ◽  
Computer Network ◽  
Connected Components ◽  
Message Complexity ◽  
Edge Connectivity ◽  
Worst Case ◽  
Dense Networks

A distributed algorithm for finding the cut-edges and the 3-edge-connected components of an asynchronous computer network is presented. For a network with n nodes and m links, the algorithm has worst-case [Formula: see text] time and O(m + nhT) message complexity, where hT < n. The algorithm is message optimal when [Formula: see text] which includes dense networks (i.e. m ∈ Θ(n2)). The previously best known distributed algorithm has a worst-case O(n3) time and message complexity.

Efficient distributed algorithm to solve updating minimum spanning tree problem

1992 ◽  
Vol 23 (3) ◽  
pp. 1-12 ◽  
Author(s):  
Jungho Park ◽  
Ken'Ichi Hagihara ◽  
Nobuki Tokura ◽  
Toshimitsu Masuzawa
Keyword(s):  
Distributed Algorithm ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Minimum Spanning Tree Problem

The Problem of Scheduling Parallel Computations of Multibody Dynamic Analysis Is NP-Hard

1996 ◽  
Author(s):  
Jin-Fan Liu ◽  
Karim A. Abdel-Malek
Keyword(s):  
Dynamic Analysis ◽  
Spanning Tree ◽  
Minimum Weight ◽  
Computational Cost ◽  
Parallel Computations ◽  
Np Hard ◽  
Multibody Dynamic ◽  
Np Hard Problem ◽  
Np Complete ◽  
Minimum Weight Spanning Tree

Abstract A formulation of a graph problem for scheduling parallel computations of multibody dynamic analysis is presented. The complexity of scheduling parallel computations for a multibody dynamic analysis is studied. The problem of finding a shortest critical branch spanning tree is described and transformed to a minimum radius spanning tree, which is solved by an algorithm of polynomial complexity. The problems of shortest critical branch minimum weight spanning tree (SCBMWST) and the minimum weight shortest critical branch spanning tree (MWSCBST) are also presented. Both problems are shown to be NP-hard by proving that the bounded critical branch bounded weight spanning tree (BCBBWST) problem is NP-complete. It is also shown that the minimum computational cost spanning tree (MCCST) is at least as hard as SCBMWST or MWSCBST problems, hence itself an NP-hard problem. A heuristic approach to solving these problems is developed and implemented, and simulation results are discussed.

Distributed Algorithms for Delay Bounded Minimum Energy Wireless Broadcasting

2010 ◽  
pp. 1677-1697
Author(s):  
Serkan Çiftlikli ◽  
Figen Öztoprak ◽  
Özgür Erçetin ◽  
Kerem Bülbül
Keyword(s):  
Distributed Algorithms ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Minimum Energy ◽  
Transmission Power ◽  
Message Complexity ◽  
Delay Constraint ◽  
Delay Bound ◽  
Lower Power ◽  
Tree Expansion

In this article, we investigate two different distributed algorithms for constructing a minimum power broadcast tree with a maximum depth ? which corresponds to the maximum tolerable end-to-end delay in the network. Distributed Tree Expansion (DTE) is based on an implementation of a distributed minimum spanning tree algorithm in which the tree grows at each iteration by adding a node that can cover the maximum number of currently uncovered nodes in the network with minimum incremental transmission power and without violating the delay constraint. In Distributed Link Substitution (DLS), given a feasible broadcast tree, the solution is improved by replacing expensive transmissions by transmissions at lower power levels while reserving the feasibility of the tree with respect to the delay bound. Although DTE increases the message complexity to O(n3) from O(n2?) in a network of size n, it provides up to 50% improvement in total expended power compared to DLS.

The Minimum Stretch Spanning Tree Problem for Hamming Graphs and Higher-Dimensional Grids

2020 ◽  
Vol 20 (01) ◽  
pp. 2050004
Author(s):  
LAN LIN ◽  
YIXUN LIN
Keyword(s):  
Communication Networks ◽  
Spanning Tree ◽  
Optimization Problem ◽  
Maximum Distance ◽  
Np Hard ◽  
Graph Invariant ◽  
Minimum Value ◽  
Higher Dimensional ◽  
Hamming Graphs

The minimum stretch spanning tree problem for a graph G is to find a spanning tree T of G such that the maximum distance in T between two adjacent vertices is minimized. The minimum value of this optimization problem gives rise to a graph invariant σ(G), called the tree-stretch of G. The problem has been proved NP-hard. In this paper we present a general approach to determine the exact values σ(G) for a series of typical graphs arising from communication networks, such as Hamming graphs and higher-dimensional grids (including hypercubes).

Sign in / Sign up

Export Citation Format

Share Document