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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 : : : : : ..."
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Cited by 60 (1 self)
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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 ..."
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Cited by 42 (3 self)
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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 ...
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 ..."
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Cited by 39 (1 self)
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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.
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 about 1:64 i ..."
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Cited by 35 (2 self)
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. 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....
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 ..."
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Cited by 23 (1 self)
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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. ..."
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Cited by 12 (1 self)
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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.
Design and Analysis of Algorithms: Course Notes
"... Contents 1 Overview of Course 3 1.1 Amortized Analysis : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 3 2 Splay Trees 5 2.1 Use of Splay Operations : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 2.2 Time for a Splay Operation ..."
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Cited by 1 (0 self)
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Contents 1 Overview of Course 3 1.1 Amortized Analysis : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 3 2 Splay Trees 5 2.1 Use of Splay Operations : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 2.2 Time for a Splay Operation : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 6 3 Amortized Time for Splay Trees 8 3.1 Additional notes : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 11 4 Maintaining Disjoint Set's 12 4.1 Disjoint set operations: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 12 4.2 Data structure: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 12 4.3 Union by rank : : : : : : : : : : : : : : : : :
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, ..."
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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.
c The Operations Research Society of Japan SOLVING CONSTRAINED TWOFACILITY LOCATION PROBLEMS Atsuo Suzuki
, 2013
"... Abstract A general approach to optimally solve multiple facility location problems based on the “Big Triangle Small Triangle ” approach to solving single facility problems is proposed. The proposed procedure is especially effective when the solution is constrained to a given polygon such as the conv ..."
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Abstract A general approach to optimally solve multiple facility location problems based on the “Big Triangle Small Triangle ” approach to solving single facility problems is proposed. The proposed procedure is especially effective when the solution is constrained to a given polygon such as the convex hull of demand points. The procedure is tested on the two facilities Weber problem with attraction and repulsion (WAR) with excellent computational results.