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Minimizing Total Busy Time in Parallel Scheduling with Application to Optical Networks
"... We consider a scheduling problem in which a bounded number of jobs can be processed simultaneously by a single machine. The input is a set of n jobs J = {J1,...,Jn}. Each job, Jj, is associated with an interval [sj,cj] along which it should be processed. Also given is the parallelism parameter g ≥ 1 ..."
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Cited by 9 (4 self)
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We consider a scheduling problem in which a bounded number of jobs can be processed simultaneously by a single machine. The input is a set of n jobs J = {J1,...,Jn}. Each job, Jj, is associated with an interval [sj,cj] along which it should be processed. Also given is the parallelism parameter g ≥ 1, which is the maximal number of jobs that can be processed simultaneously by a single machine. Each machine operates along a contiguous time interval, called its busy interval, which contains all the intervals corresponding to the jobs it processes. The goal is to assign the jobs to machines such that the total busy time of the machines is minimized. The problem is known to be NPhard already for g = 2. We present a 4approximation algorithm for general instances, and approximation algorithms with improved ratios for instances with bounded lengths, for instances where any two intervals intersect, and for instances where no interval is properly contained in another. Our study has important application in optimizing the switching costs of optical networks.
Approximating the Traffic Grooming Problem in Tree and Star Networks (Extended Abstract)
, 2006
"... We consider the problem of grooming paths in alloptical networks with tree topology so as to minimize the switching cost, measured by the total number of used ADMs. We first present efficient approximation algorithms with approximation factor of 2ln(δ · g)+o(ln(δ · g)) for any fixed node degree b ..."
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Cited by 4 (0 self)
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We consider the problem of grooming paths in alloptical networks with tree topology so as to minimize the switching cost, measured by the total number of used ADMs. We first present efficient approximation algorithms with approximation factor of 2ln(δ · g)+o(ln(δ · g)) for any fixed node degree bound δ and grooming factor g, and2lng + o(ln g) in unbounded degree directed trees, respectively. In the attempt of extending our results to general undirected trees we completely characterize the complexity of the problem in star networks by providing polynomial time optimal algorithms for g ≤ 2 and proving the intractability of the problem for any fixed g>2. While for general topologies the problem was known to be NPhard g not constant, the complexity for fixed values of g was still an open question.
Approximating the Revenue Maximization Problem with Sharp Demands
"... Abstract. We consider the revenue maximization problem with sharp multidemand, in which m indivisible items have to be sold to n potential buyers. Each buyer i is interested in getting exactly di items, and each item j gives a benefit vij to buyer i. We distinguish between unrelated and related val ..."
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Abstract. We consider the revenue maximization problem with sharp multidemand, in which m indivisible items have to be sold to n potential buyers. Each buyer i is interested in getting exactly di items, and each item j gives a benefit vij to buyer i. We distinguish between unrelated and related valuations. In the former case, the benefit vij is completely arbitrary, while, in the latter, each item j has a quality qj, each buyer i has a value vi and the benefit vij is defined as the product viqj. The problem asks to determine a price for each item and an allocation of bundles of items to buyers with the aim of maximizing the total revenue, that is, the sum of the prices of all the sold items. The allocation must be envyfree, that is, each buyer must be happy with her assigned bundle and cannot improve her utility. We first prove that, for related valuations, the problem cannot be approximated to a factor O(m 1−ɛ), for any ɛ> 0, unless P = NP and that such result is asymptotically tight. In fact we provide a simple mapproximation algorithm even for unrelated valuations. We then focus on an interesting subclass of ”proper ” instances, that do not contain buyers a priori known not being able to receive any item. For such instances, we design an interesting 2approximation algorithm and show that no (2 − ɛ)approximation is possible for any 0 < ɛ ≤ 1, unless P = NP. We observe that it is possible to efficiently check if an instance is proper, and if discarding useless buyers is allowed, an instance can be made proper in polynomial time, without worsening the value of its optimal solution. 1
Approximate MinPower Strong Connectivity
"... Given a directed simple graph G = (V,E) and a cost function c: E → R+, the power of a vertex u in a directed spanning subgraph H is given by pH(u) = max uv∈E(H)c(uv), and corresponds to the energy consumption required for wireless node u to transmit to all nodes v with uv ∈ E(H). The power of H is ..."
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Cited by 4 (1 self)
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Given a directed simple graph G = (V,E) and a cost function c: E → R+, the power of a vertex u in a directed spanning subgraph H is given by pH(u) = max uv∈E(H)c(uv), and corresponds to the energy consumption required for wireless node u to transmit to all nodes v with uv ∈ E(H). The power of H is given by p(H) = ∑ u∈V pH(u). Power Assignment seeks to minimize p(H) while H satisfies some connectivity constraint. In this paper, we assume E is bidirected (for every directed edge e ∈ E, the opposite edge exists and has the same cost), while H is required to be strongly connected. This is the original power assignment problem introduced by Chen and Huang in 1989, who proved that a bidirected minimum spanning tree has approximation ratio at most 2 (this is tight). In Approx 2010, we introduced a greedy approximation algorithm and claimed a ratio of 1.992. Here we improve the algorithm’s analysis to 1.85, combining techniques from RobinsZelikovsky (2000) for Steiner Tree, and Caragiannis, Flammini, and Moscardelli (2007) for the broadcast version of Power Assignment, together with a simple idea inspired by Byrka, Grandoni, Rothvoß, and Sanità (2010). The proof also shows that a natural linear programming relaxation, introduced by Calinescu and Qiao in Infocom 2012, has integrality gap at most 1.85.
A 6/5approximation algorithm for the maximum 3cover problem
 In Proceedings of the 33rd International Symposium on Mathematical Foundations of Computer Science (MFCS ’08
, 2008
"... Abstract. In the maximum cover problem, we are given a collection of sets over a ground set of elements and a positive integer w, and we are asked to compute a collection of at most w sets whose union contains the maximum number of elements from the ground set. This is a fundamental combinatorial op ..."
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Abstract. In the maximum cover problem, we are given a collection of sets over a ground set of elements and a positive integer w, and we are asked to compute a collection of at most w sets whose union contains the maximum number of elements from the ground set. This is a fundamental combinatorial optimization problem with applications to resource allocation. We study the simplest APXhard variant of the problem where all sets are of size at most 3 and we present a 6/5approximation algorithm, improving the previously best known approximation guarantee. Our algorithm is based on the idea of first computing a large packing of disjoint sets of size 3 and then augmenting it by performing simple local improvements. 1
ProjectTeam Mascotte Méthodes Algorithmiques, Simulation et Combinatoire pour l’OpTimisation des
"... c t i v it y e p o r t 2009 Table of contents ..."
Networks and Telecommunications
"... 6.1.1.2. Wavelength assignment in WDM networks 6 6.1.1.3. Mutlioperators microwave backhaul networks 7 6.1.2. Energy efficiency 7 6.1.2.1. Energy aware routing with redundancy elimination 7 ..."
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6.1.1.2. Wavelength assignment in WDM networks 6 6.1.1.3. Mutlioperators microwave backhaul networks 7 6.1.2. Energy efficiency 7 6.1.2.1. Energy aware routing with redundancy elimination 7
Results 1  10
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