Results 1  10
of
27
Modifying Edges of a Network to Obtain Short Subgroups
, 1996
"... This paper considers problems of the following type: We are given an edge weighted graph G = (V, E). It is assumed that each edge e of the given network has an associated function c_e that specifies the cost of shortening the edge by a given amount and that there is a budget B on the total reduction ..."
Abstract

Cited by 12 (2 self)
 Add to MetaCart
This paper considers problems of the following type: We are given an edge weighted graph G = (V, E). It is assumed that each edge e of the given network has an associated function c_e that specifies the cost of shortening the edge by a given amount and that there is a budget B on the total reduction cost. The goal is to develop a reduction strategy satisfying the budget constraint so that the total length of a minimum spanning tree in the modified network is the smallest possible over all reduction strategies that obey the budget constraint. We show that in general the problem of computing an optimal reduction strategy for modifying the network as above is NPhard even for simple classes of graphs and linear functions c_e. We present the first polynomial time approximation algorithms for the problem, where the cost functions c_e are allowed to be taken from a broad class of functions. We also present improved approximation algorithms for the class of treewidthbounded graphs when the cost functions are linear...
Approximation Algorithms for Certain Network Improvement Problems
 J. Comb. Optim
, 1998
"... . We study budget constrained network upgrading problems. Such problems aim at nding optimal strategies for improving a network under some cost measure subject to certain budget constraints. Given an edge weighted graph G = (V; E), in the edge based upgrading model, it is assumed that each edge e of ..."
Abstract

Cited by 9 (0 self)
 Add to MetaCart
(Show Context)
. We study budget constrained network upgrading problems. Such problems aim at nding optimal strategies for improving a network under some cost measure subject to certain budget constraints. Given an edge weighted graph G = (V; E), in the edge based upgrading model, it is assumed that each edge e of the given network also has an associated function ce (t) that species the cost of upgrading the edge by an amount t. A reduction strategy species for each edge e the amount by which the length `(e) is to be reduced. In the node based upgrading model, a node v can be upgraded at an expense of c(v). Such an upgrade reduces the delay of each edge incident on v. For a given budget B, the goal is to nd an improvement strategy such that the total cost of reduction is at most the given budget B and the cost of a subgraph (e.g. minimum spanning tree) under the modied edge lengths is the best over all possible strategies which obey the budget constraint. After providing a brief overview of the...
Efficient Algorithms for Robustness in Matroid Optimization
 PROCEEDINGS OF THE EIGHTH ANNUAL ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS (NEW
, 1996
"... The robustness function of a matroid measures the maximum increase in the weight of its minimum weight bases that can be produced by increases of a given total cost on the weights of its elements. We present an algorithm for computing this function, that runs in strongly polynomial time for matroids ..."
Abstract

Cited by 8 (1 self)
 Add to MetaCart
(Show Context)
The robustness function of a matroid measures the maximum increase in the weight of its minimum weight bases that can be produced by increases of a given total cost on the weights of its elements. We present an algorithm for computing this function, that runs in strongly polynomial time for matroids in which independence can be tested in strongly polynomial time. We identify key properties of transversal, scheduling and partition matroids, and exploit them to design robustness algorithms that are more efficient than our general algorithm.
Bottleneck Capacity Expansion Problems With General Budget Constraints
, 2000
"... This paper presents a unified approach for bottleneck capacity expansion problems. In the bottleneck capacity expansion problem, BCEP, we are given a finite ground set E, a family F of feasible subsets of E and a nonnegative real capacity b c e for all e 2 E. Moreover, we are given monotone increasi ..."
Abstract

Cited by 8 (1 self)
 Add to MetaCart
This paper presents a unified approach for bottleneck capacity expansion problems. In the bottleneck capacity expansion problem, BCEP, we are given a finite ground set E, a family F of feasible subsets of E and a nonnegative real capacity b c e for all e 2 E. Moreover, we are given monotone increasing cost functions f e for increasing the capacity of the elements e 2 E as well as a budget B. The task is to determine new capacities c e b c e such that the objective function given by max F2F min e2F c e is maximized under the side constraint that the overall expansion cost does not exceed the budget B. We introduce an algebraic model for defining the overall expansion cost and for formulating the budget constraint. This models allows to capture various types of budget constraints in one general model. Moreover, we discuss solution approaches for the general bottleneck capacity expansion problem. For an important subclass of bottleneck capacity expansion problems we propose ...
Finding the k most vital edges with respect to minimum spanning trees for fixed k
 Discrete Applied Mathematics
, 1998
"... k ..."
(Show Context)
Design is as easy as optimization
 In 33rd International Colloquium on Automata, Languages and Programming (ICALP
, 2006
"... We consider the class of maxmin and minmax optimization problems subject to a global budget (or weight) constraint and we undertake a systematic algorithmic and complexitytheoretic study of such problems, which we call problems design problems. Every optimization problem leads to a natural design ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
We consider the class of maxmin and minmax optimization problems subject to a global budget (or weight) constraint and we undertake a systematic algorithmic and complexitytheoretic study of such problems, which we call problems design problems. Every optimization problem leads to a natural design problem. Our main result uses techniques of FreundSchapire [FS99] from learning theory, and its generalizations, to show that for a large class of optimization problems, the design version is as easy as the optimization version. We also observe a close relationship between design problems and packing problems; this yields relationships between fractional packing of spanning and Steiner trees in a graph, the strength of the graph, and the integrality gap of the bidirected cut relaxation for the graph. 1
On BudgetConstrained Flow Improvement
, 1998
"... This paper investigates the complexity of budgetconstrained flow improvement problems. We are given a directed graph with capacities on the edges which can be increased at linear costs up to some upper bounds. The problem is to increase the capacities within budget restrictions such that the flow ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
This paper investigates the complexity of budgetconstrained flow improvement problems. We are given a directed graph with capacities on the edges which can be increased at linear costs up to some upper bounds. The problem is to increase the capacities within budget restrictions such that the flow from the source to the sink vertex is maximized. We show that the problem can be solved in polynomial time even if the improvement strategy is required to be integral. On the other hand, if the capacity of an edge must either be increased to the upper bound or left unchanged, then the problem turns NPhard even on seriesparallel graphs and strongly NPhard on bipartite graphs. For the class seriesparallel graphs we provide a fully polynomial approximation scheme for this problem.
Modifying Networks to Obtain Low Cost Trees
 In WG: GraphTheoretic Concepts in Computer Science, International Workshop WG
, 1996
"... We consider the problem of reducing the edge lengths of a given network so that the modified network has a spanning tree of small total length. It is assumed that each edge e of the given network has an associated function Ce that specifies the cost of shortening the edge by a given amount and that ..."
Abstract

Cited by 5 (4 self)
 Add to MetaCart
(Show Context)
We consider the problem of reducing the edge lengths of a given network so that the modified network has a spanning tree of small total length. It is assumed that each edge e of the given network has an associated function Ce that specifies the cost of shortening the edge by a given amount and that there is a budget B on the total reduction cost. The goal is to develop a reduction strategy satisfying the budget constraint so that the total length of a minimum spanning tree in the modified network is the smallest possible over all reduction strategies that obey the budget constraint. We show that in general the problem of computing optimal reduction strategy for modifying the network as above is NPhard and present the first polynomial time approximation algorithms for the problem, where the cost functions Ce are allowed to be taken from a broad class of functions. We also present improved approximation algorithms for the class of treewidthbounded graphs when the cost functions are li...
Improving minimum cost spanning trees by upgrading nodes
 J. Alg
, 1999
"... This Article is brought to you for free and open access by Research Showcase @ CMU. It has been accepted for inclusion in Tepper School of Business ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
This Article is brought to you for free and open access by Research Showcase @ CMU. It has been accepted for inclusion in Tepper School of Business