Results 1  10
of
15
Approximation Algorithms for Finding Highly Connected Subgraphs
, 1996
"... Contents 1 Introduction 2 1.1 Outline of Chapter : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 3 2 EdgeConnectivity Problems 3 2.1 Weighted EdgeConnectivity : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 3 2.2 Unweighted EdgeConnectivity : : : : : ..."
Abstract

Cited by 63 (1 self)
 Add to MetaCart
Contents 1 Introduction 2 1.1 Outline of Chapter : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 3 2 EdgeConnectivity Problems 3 2.1 Weighted EdgeConnectivity : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 3 2.2 Unweighted EdgeConnectivity : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 4 2.2.1 2 EdgeConnectivity : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 4 2.2.2 EdgeConnectivity : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 8 3 VertexConnectivity Problems 11 3.1 Weighted VertexConnectivity : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 11 3.2 Unweighted VertexConnectivity : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 12 3.2.1 2 VertexConnectivity : : : : : : : : : : : : : : : : :
Combinatorial algorithms for DNA sequence assembly
 Algorithmica
, 1993
"... The trend towards very large DNA sequencing projects, such as those being undertaken as part of the human genome initiative, necessitates the development of efficient and precise algorithms for assembling a long DNA sequence from the fragments obtained by shotgun sequencing or other methods. The seq ..."
Abstract

Cited by 45 (3 self)
 Add to MetaCart
(Show Context)
The trend towards very large DNA sequencing projects, such as those being undertaken as part of the human genome initiative, necessitates the development of efficient and precise algorithms for assembling a long DNA sequence from the fragments obtained by shotgun sequencing or other methods. The sequence reconstruction problem that we take as our formulation of DNA sequence assembly is a variation of the shortest common superstring problem, complicated by the presence of sequencing errors and reverse complements of fragments. Since the simpler superstring problem is NPhard, any efficient reconstruction procedure must resort to heuristics. In this paper, however, a four phase approach based on rigorous design criteria is presented, and has been found to be very accurate in practice. Our method is robust in the sense that it can accommodate high sequencing error rates and list a series of alternate solutions in the event that several appear equally good. Moreover it uses a limited form ...
Approximating The Minimum Equivalent Digraph
, 1995
"... . The MEG (minimum equivalent graph) problem is the following: "Given a directed graph, find a smallest subset of the edges that maintains all reachability relations between nodes." This problem is NPhard; this paper gives an approximation algorithm achieving a performance guarantee of ab ..."
Abstract

Cited by 42 (2 self)
 Add to MetaCart
. The MEG (minimum equivalent graph) problem is the following: "Given a directed graph, find a smallest subset of the edges that maintains all reachability relations between nodes." This problem is NPhard; this paper gives an approximation algorithm achieving a performance guarantee of about 1:64 in polynomial time. The algorithm achieves a performance guarantee of 1:75 in the time required for transitive closure. The heart of the MEG problem is the minimum SCSS (strongly connected spanning subgraph) problem  the MEG problem restricted to strongly connected digraphs. For the minimum SCSS problem, the paper gives a practical, nearly lineartime implementation achieving a performance guarantee of 1:75. The algorithm and its analysis are based on the simple idea of contracting long cycles. The analysis applies directly to 2Exchange, a general "local improvement" algorithm, showing that its performance guarantee is 1:75. AMS subject classifications. 68R10, 90C27, 90C35, 05C85, 68Q20....
Balancing Minimum Spanning Trees and ShortestPath Trees
, 2002
"... We give a simple algorithm to find a spanning tree that simultaneously approximates a shortestpath tree and a minimum spanning tree. The algorithm provides a continuous tradeoff: given the two trees and a fl? 0, the algorithm returns a spanning tree in which the distance between any vertex and the ..."
Abstract

Cited by 39 (1 self)
 Add to MetaCart
(Show Context)
We give a simple algorithm to find a spanning tree that simultaneously approximates a shortestpath tree and a minimum spanning tree. The algorithm provides a continuous tradeoff: given the two trees and a fl? 0, the algorithm returns a spanning tree in which the distance between any vertex and the root of the shortestpath tree is at most 1 + p 2fl times the shortestpath distance, and yet the total weight of the tree is at most 1 + p 2=fl times the weight of a minimum spanning tree. Our algorithm runs in linear time and obtains the bestpossible tradeoff. It can be implemented on a CREW PRAM to run in logarithmic time using one processor per vertex.
Restoration Algorithms for Virtual Private Networks in the Hose Model
, 2002
"... A Virtual Private Network (VPN) aims to emulate the services provided by a private network over the shared Internet. The endpoints of a VPN are connected using abstractions such as Virtual Channels (VCs) of ATM or Label Switching Paths (LSPs) of MPLS technologies. Reliability of an endtoend VPN co ..."
Abstract

Cited by 25 (1 self)
 Add to MetaCart
A Virtual Private Network (VPN) aims to emulate the services provided by a private network over the shared Internet. The endpoints of a VPN are connected using abstractions such as Virtual Channels (VCs) of ATM or Label Switching Paths (LSPs) of MPLS technologies. Reliability of an endtoend VPN connection depends on the reliability of the links and nodes in the fixed path that it traverses in the network. In order to ensure service quality and availability in a VPN, seamless recovery from failures is essential. This work considers the problem of fast recovery in the recently proposed VPN hose model. In the hose model bandwidth is reserved for traffic aggregates instead of pairwise specifications to allow any traffic pattern among the VPN endpoints. This work assumes that the VPN endpoints are connected using a tree structure and at any time, at most one tree link can fail (i.e., single link failure model). A restoration algorithm must select asetofbackup edges and allocate necessary bandwidth on them in advance, so that the traffic disrupted by failure of a primary edge can be rerouted via backup paths. We aim at designing an optimal restoration algorithm to minimize the total bandwidth reserved on the backup edges. This problem is a variant of optimal graph augmentation problem which is NPComplete. Thus, we present a polynomialtime approximation algorithm that guarantees a solution which is at most 16 times of the optimum. The algorithm is based on designing two reductions to convert the original problem to one of adding minimum cost edges to the VPN tree so that the resulting graph is 2connected, which can be solved in polynomial time using known algorithms. The two reductions introduce approximation factors of 8 and 2, respectively, thus resulting in a 16appro...
Arborescence optimization problems solvable by Edmonds’ algorithm
 Theoretical Computer Science
, 2003
"... Abstract. We consider a general class of optimization problems regarding spanning trees in directed graphs (arborescences). We present an algorithm for solving such problems, which can be considered as a generalization of Edmonds ’ algorithm for the solution of the minimumcost arborescence problem. ..."
Abstract

Cited by 13 (2 self)
 Add to MetaCart
(Show Context)
Abstract. We consider a general class of optimization problems regarding spanning trees in directed graphs (arborescences). We present an algorithm for solving such problems, which can be considered as a generalization of Edmonds ’ algorithm for the solution of the minimumcost arborescence problem. The considered class of optimization problems includes as special cases the standard minimumcost arborescence problem, the bottleneck and the lexicographically optimal arborescence problem.
On the Construction of a Strongly Connected Broadcast Arborescence with Bounded Transmission Delay
"... Abstract—Energy conservation is an important concern in wireless networks. Many algorithms for constructing a broadcast tree with minimum energy consumption and other goals have been developed. However, no previous research work considers the total energy consumption and transmission delays of the b ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Abstract—Energy conservation is an important concern in wireless networks. Many algorithms for constructing a broadcast tree with minimum energy consumption and other goals have been developed. However, no previous research work considers the total energy consumption and transmission delays of the broadcast tree simultaneously. In this paper, based on anð; Þtree, a novel concept to wireless networks, we define a new Strongly connected Broadcast Arborescence with bounded Transmission delay (SBAT) problem and design the Strongly connected Broadcast Arborescence (SBA) algorithm with linear running time to construct a strongly connected broadcast tree with bounded total power, while satisfying the constraint that the transmission delays between the source and the other hosts are also bounded. We also propose the distributed version of the SBA algorithm. The theoretical analysis and simulation results show that the SBA algorithm gives a proper solution to the SBAT problem. Index Terms—Wireless networks, routing protocols, network management, distributed applications, algorithm design and analysis. 1
RankPairing Heaps
"... Abstract. We introduce the rankpairing heap, a heap (priority queue) implementation that combines the asymptotic efficiency of Fibonacci heaps with much of the simplicity of pairing heaps. Unlike all other heap implementations that match the bounds of Fibonacci heaps, our structure needs only one c ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Abstract. We introduce the rankpairing heap, a heap (priority queue) implementation that combines the asymptotic efficiency of Fibonacci heaps with much of the simplicity of pairing heaps. Unlike all other heap implementations that match the bounds of Fibonacci heaps, our structure needs only one cut and no other structural changes per key decrease; the trees representing the heap can evolve to have arbitrary structure. Our initial experiments indicate that rankpairing heaps perform almost as well as pairing heaps on typical input sequences and better on worstcase sequences. 1
LAGRANGIANBASED COLUMN GENERATION FOR THE NODE CAPACITATED INTREE PACKING PROBLEM
, 2011
"... Abstract In this paper, we deal with the node capacitated intree packing problem. The input consists of a directed graph, a root node, a node capacity function and edge consumption functions for heads and tails. The problem is to find a subset of rooted spanning intrees and their packing numbers, ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract In this paper, we deal with the node capacitated intree packing problem. The input consists of a directed graph, a root node, a node capacity function and edge consumption functions for heads and tails. The problem is to find a subset of rooted spanning intrees and their packing numbers, where the packing number of an intree is the number of times it is packed, so as to maximize the sum of packing numbers under the constraint that the total consumption of the packed intrees at each node does not exceed the capacity of the node. This problem is known to be NPhard. Previously, we proposed a twophase heuristic algorithm for this problem. The algorithm generates promising candidate intrees to be packed in the first phase and computes the packing number of each intree in the second phase. In this paper, we improve the first phase algorithm by using Lagrangian relaxation instead of LP (linear programming) relaxation. We conducted computational experiments on graphs used in related papers and on randomly generated instances. The results indicate that our new algorithm generates intrees faster than our previous algorithm and obtains better solutions than existing algorithms without generating many intrees.