Computational complexity of approximation algorithms for combinatorial problems

Gens, George; Levner, Eugene

doi:10.1007/3-540-09526-8_26

Cited by 47 publications

(37 citation statements)

References 3 publications

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“…as it is composed of n − 1 executions of algorithm A of Theorem 4.4 which requires O(k) time, and n − 1 executions of algorithm from [22] which requires O(…”

Section: K Imentioning

confidence: 99%

Flow Problems in Multi-Interface Networks

D’Angelo¹,

Stefano

Navarra

2014

IEEE Trans. Comput.

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Abstract-In heterogeneous networks, devices communicate by means of multiple wired or wireless interfaces. By switching among interfaces or by combining the available ones, each device might establish several connections. A connection may be established when the devices at its endpoints share at least one active interface.In this paper, we consider two fundamental optimization problems. In the first one (Maximum Flow in Multi-Interface Networks, MFMI), we aim to establish the maximal bandwidth that can be guaranteed between two given nodes of the input network. In the second problem (Minimum-Cost Flow in MultiInterface Networks, MCFMI), we look for activating the cheapest set of interfaces among a network in order to guarantee a minimum bandwidth B of communication between two specified nodes. We show that MFMI is polynomially solvable while MCFMI is NP -hard even for a bounded number of different interfaces and bounded degree networks. Moreover, we provide polynomial approximation algorithms for MCFMI and exact algorithms for relevant sub-problems. Finally, we experimentally analyze the proposed approximation algorithm, showing that in practical cases it guarantees a low approximation ratio.

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“…as it is composed of n − 1 executions of algorithm A of Theorem 4.4 which requires O(k) time, and n − 1 executions of algorithm from [22] which requires O(…”

Section: K Imentioning

confidence: 99%

Flow Problems in Multi-Interface Networks

D’Angelo¹,

Stefano

Navarra

2014

IEEE Trans. Comput.

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“…The reduction is approximation preserving and so we are done as there is a fully polynomial time approximation scheme for the minimization knapsack problem [20].…”

Section: Additive Approximation Guaranteesmentioning

confidence: 99%

Computational Aspects of Multimarket Price Wars

Thain

Vetta

2009

Lecture Notes in Computer Science

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Abstract. We consider the complexity of decision making with regards to predatory pricing in multimarket oligopoly models. Specifically, we present multimarket extensions of the classical single-market models of Bertrand, Cournot and Stackelberg, and introduce the War Chest Minimization Problem. This is the natural problem of deciding whether a firm has a sufficiently large war chest to win a price war. On the negative side we show that, even with complete information, it is hard to obtain any multiplicative approximation guarantee for this problem. Moreover, these hardness results hold even in the simple case of linear demand, price, and cost functions. On the other hand, we give algorithms with arbitrarily small additive approximation guarantees for the Bertrand and Stackelberg multimarket models with linear demand, price, and cost functions. Furthermore, in the absence of fixed costs, this problem is solvable in polynomial time in all our models.

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“…Previous work on the MKP and other knapsack related problems assume that (i) all items of the same type have to be placed in the same knapsack, and (ii) there is no limit on the number of different types of items that can be placed in one knapsack (see, e.g., [3], [7], [15], [20] and detailed surveys in [18] and [19]). …”

Section: Related Workmentioning

confidence: 99%

“…That is, for any ε > 0, a (1 − ε)-approximation to the optimal solution can be found in O(n/ε 2 ), where n is the number of items [6], [7]. In contrast, the MKP is NP-hard in the strong sense, therefore it is unlikely to have an FPAS, unless P = NP [19].…”

Section: Related Workmentioning

confidence: 99%

On Two Class-Constrained Versions of the Multiple Knapsack Problem

Shachnai

Tamir

2001

Algorithmica

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Abstract. We study two variants of the classic knapsack problem, in which we need to place items of different types in multiple knapsacks; each knapsack has a limited capacity, and a bound on the number of different types of items it can hold: in the class-constrained multiple knapsack problem (CMKP) we wish to maximize the total number of packed items; in the fair placement problem (FPP) our goal is to place the same (large) portion from each set. We look for a perfect placement, in which both problems are solved optimally. We first show that the two problems are NP-hard; we then consider some special cases, where a perfect placement exists and can be found in polynomial time. For other cases, we give approximate solutions. Finally, we give a nearly optimal solution for the CMKP. Our results for the CMKP and the FPP are shown to provide efficient solutions for two fundamental problems arising in multimedia storage subsystems.

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Computational complexity of approximation algorithms for combinatorial problems

Cited by 47 publications

References 3 publications

Flow Problems in Multi-Interface Networks

Flow Problems in Multi-Interface Networks

Computational Aspects of Multimarket Price Wars

On Two Class-Constrained Versions of the Multiple Knapsack Problem

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