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Increasing the Weight of Minimum Spanning Trees
, 1996
"... The problems of computing the maximum increase in the weight of the minimum spanning trees of a graph caused by the removal of a given number of edges, or by finite increases in the weights of the edges, are investigated. For the case of edge removals, the problem is shown to be NPhard and an \Omeg ..."
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Cited by 26 (1 self)
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The problems of computing the maximum increase in the weight of the minimum spanning trees of a graph caused by the removal of a given number of edges, or by finite increases in the weights of the edges, are investigated. For the case of edge removals, the problem is shown to be NPhard and an \Omega\Gamma/ = log k)approximation algorithm is presented for it, where k is the number of edges to be removed. The second problem is studied assuming that the increase in the weight of an edge has an associated cost proportional to the magnitude of the change. An O(n 3 m 2 log(n 2 =m)) time algorithm is presented to solve it. 1 Introduction Consider a communication network in which information is broadcast over a minimum spanning tree. There are applications for which it is important to determine the maximum degradation in the performance of the broadcasting protocol that can be expected as a result of traffic fluctuations and link failures [25]. Also, there are several combinatorial op...
Inverse Combinatorial Optimization: A Survey on Problems, Methods, and Results
 TO APPEAR IN JOURNAL OF COMBINATORIAL OPTIMIZATION
"... Given a (combinatorial) optimization problem and a feasible solution to it, the corresponding inverse optimization problem is to find a minimal adjustment of the cost function such that the given solution becomes optimum. Several such problems have been studied in the last ten years. After formalizi ..."
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Cited by 25 (0 self)
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Given a (combinatorial) optimization problem and a feasible solution to it, the corresponding inverse optimization problem is to find a minimal adjustment of the cost function such that the given solution becomes optimum. Several such problems have been studied in the last ten years. After formalizing the notion of an inverse problem and its variants, we present various methods for solving them. Then we discuss the problems considered in the literature and the results that have been obtained. Finally, we formulate some open problems.
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 ..."
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Cited by 8 (1 self)
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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 ...
Inverse Optimization: A Survey on Problems, Methods, and Results
 J. COMBIN. OPT
, 2004
"... Given a (combinatorial) optimization problem and a feasible solution to it, the corresponding inverse optimization problem is to nd a minimal adjustment of the parameters of the problem (costs, capacities, . . . ) such that the given solution becomes optimum. Several such problems have been studi ..."
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Cited by 7 (0 self)
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Given a (combinatorial) optimization problem and a feasible solution to it, the corresponding inverse optimization problem is to nd a minimal adjustment of the parameters of the problem (costs, capacities, . . . ) such that the given solution becomes optimum. Several such problems have been studied in the last ten years. After formalizing the notion of an inverse problem and its variants, we present various methods for solving them. Then we discuss the problems considered in the literature and the results that have been obtained. Finally, we formulate some open problems.
On Matching Robustness
, 2007
"... We introduce the notion of robustness of the minimumweight perfect matching. The robustness measures how much the edge weights of a graph are allowed to change before the minimumweight matching changes. We consider two cases: when the edge weights are changed adversarially and when they are change ..."
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We introduce the notion of robustness of the minimumweight perfect matching. The robustness measures how much the edge weights of a graph are allowed to change before the minimumweight matching changes. We consider two cases: when the edge weights are changed adversarially and when they are changed randomly. We provide algorithms for computing the robustness in both cases.
On Geometric Stable Roommates and MinimumWeight Matching Robustness (Extended Abstract)
"... This paper consists of two parts, both of which address stability of perfect matchings. In the first part we consider instances of the Stable Roommates problem that arise from geometric representation of participants preferences: a participant is a point in Euclidean space, and his preference list i ..."
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This paper consists of two parts, both of which address stability of perfect matchings. In the first part we consider instances of the Stable Roommates problem that arise from geometric representation of participants preferences: a participant is a point in Euclidean space, and his preference list is given by sorted distances to the other participants. We observe that, unlike in the general case, if there are no ties in the preference lists, there always exists a unique stable matching; a simple greedy algorithm finds the matching efficiently. We show that, also contrary to the general case, the problem admits polynomialtime solution even in the case when ties are present in the preference lists. We define the notion of αstable matching: the participants are willing to switch partners only for the improvement of at least α. We prove that in general, finding αstable matchings is not easier than finding matchings, stable in the usual sense. We show that, unlike in the general case, in a threedimensional geometric stable roommates problem, a 2stable matching can be found in polynomial time. In the second part we study the “robustness” of the minimumweight perfect matching. The robustness measures how much the edge weights of a graph are allowed to be distorted before the minimumweight matching changes. We consider two cases: when the edge weights are changed adversarially and when they are changed at random. We provide algorithms for computing the robustness in both cases.
Network Design and Improvement
, 1999
"... Inspired by the fact that many combinatorial optimization problems arising in practice are NPhard, the design of efficient approximation algorithms has been a major research topic for the last years. Since we can not expect to solve any NPhard problem in polynomial time, it is meaningful to compro ..."
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Inspired by the fact that many combinatorial optimization problems arising in practice are NPhard, the design of efficient approximation algorithms has been a major research topic for the last years. Since we can not expect to solve any NPhard problem in polynomial time, it is meaningful to compromise optimality of a solution and settle for a “sufficiently good” solution that can be computed efficiently in polynomial time.