Flow Improvement and Network Flows with Fixed Costs

Krumke, Sven O.; Noltemeier, Hartmut; Schwarz, Sebastian; Wirth, Hans-Christoph; Ravi, R.

doi:10.1007/978-3-642-58409-1_15

Cited by 35 publications

(45 citation statements)

References 8 publications

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“…We prove a hardness reduction for Í Á under the assumption È AEÈ using a reduction from Set-Cover. We need a somewhat different proof than the one reported in (Krumke et al, 1998) to account for the extra restriction imposed by Í Á . For our purposes it is convenient to formulate the set cover problem as follows.…”

Section: Theorem 21 There Is a Constantmentioning

confidence: 95%

The minimum shift design problem

Gaspero

Gärtner²,

Kortsarz

et al. 2007

Ann Oper Res

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The min-SHIFT DESIGN problem (ÅË ) is an important scheduling problem that needs to be solved in many industrial contexts. The issue is to find a minimum number of shifts and the number of employees to be assigned to these shifts in order to minimize the deviation from workforce requirements.Our research considers both theoretical and practical aspects of the min-SHIFT DESIGN problem. This problem is closely related to the minimum edge-cost flow problem (Å ), a network flow variant that has many applications beyond shift scheduling. We show that ÅË reduces to a special case of Å and, exploiting this reduction, we prove a logarithmic hardness of approximation lower bound for ÅË . On the basis of these results, we propose a hybrid heuristic for the problem which relies on a greedy heuristic with a min-cost max-flow subroutine based on the network flow analogy followed by a local search algorithm that makes use of multiple neighborhood relations. An experimental analysis on structured random instances shows that the hybrid heuristic clearly outperforms our previous commercial implementation and highlights the respective merits of the composing heuristics for different performance parameters.

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Section: Theorem 21 There Is a Constantmentioning

confidence: 95%

The minimum shift design problem

Gaspero

Gärtner²,

Kortsarz

et al. 2007

Ann Oper Res

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“…For the case of zero migration cost, DAHM can be formulated as a more specific problem that is a Fixed Charge Min Cost Flow (FCMCF). FCMCF is also NP-hard [66] but, compared to MIP, more efficient approximation methods have been developed [29] (FCMCF can be solved by MIP but not vice versa). We also show that DAHM is NP-hard by reducing an NP-hard sub-case of FCMCF to it.…”

Section: Cost Minimization Is Subject To the Following Constraintsmentioning

confidence: 99%

“…In FCMCF [66] a graph G = (V, E) with nonnegative capacities capacity i and nonnegative costs w i for each edge i is given with the edge cost defined on each edge's flow f i as follows: w i = flow-cost i f i + fixed-charge i , when f i > 0 and w i = 0 when f i = 0. The question is whether there is a subset A ⊆ E of the edges of G such that the flow from the source to the sink in (V, A) is at least F and the cost is at most W .…”

Section: Cost Minimization Is Subject To the Following Constraintsmentioning

confidence: 99%

“…The question is whether there is a subset A ⊆ E of the edges of G such that the flow from the source to the sink in (V, A) is at least F and the cost is at most W . FCMCF is known to be NP-hard even on a graph with two nodes and a set of multiple edges between them [66] (this case solves Knapsack).…”

Section: Cost Minimization Is Subject To the Following Constraintsmentioning

confidence: 99%

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Sustainable Cloud Computing

Domdouzis

2015

Green Information Technology

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Energy consumption of the data centers worldwide is rapidly growing fueled by everincreasing demand for Cloud computing applications ranging from social networking to e-commerce. Understandably, ensuring energy-efficiency and sustainability of Cloud data centers without compromising performance is important for both economic and environmental reasons. In order to achieve these objectives, this dissertation develops a cyber-physical multi-tier server and workload management architecture which operates at the local and the global (geo-distributed) data center level.This dissertation devises optimization frameworks for each tier to optimize energy consumption, energy cost and carbon footprint of the data centers. The proposed solutions are aware of various energy management tradeoffs that manifest due to the cyber-physical interactions in data centers, while providing provable guarantee on the solutions' computation efficiency and energy/cost efficiency. The local data center level energy management takes into account the impact of server consolidation on the cooling energy, avoids cooling-computing power tradeoff, and optimizes the total energy (computing and cooling energy) considering the data centers' technology trends (servers' power proportionality and the cooling power efficiency). The global data center level cost management explores the diversity of the data centers to minimize the utility cost while satisfying the carbon cap requirement of the Cloud and while dealing with the adversity of the prediction error on the data center parameters. Finally, the synergy of the local and the global data center energy and cost optimization is shown to help towards achieving carbon neutrality (net-zero) in a cost efficient manner.

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“…In our setting, the objective function is indifferent to the quantity of flow on each edge, and only distinguishes between zero and non-zero flow (leading to either a fixed charge or a more involved function; see the next sections). The most closely related recent sources we have encountered in the literature on network design are [9,15,16,30]. The major difference with each of these is the fact that we also impose (a) side constraints on node flow, namely that it be equal to r ik or a k (see Equations (1) and (2)), as well as (b) acyclicity.…”

Section: Network Designmentioning

confidence: 99%

An Investigation of Resource-Allocation Decisions by Means of Project Networks

Leus

2007

SSRN Journal

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This paper investigates the relationship between resource allocation and ES-policies, which are a type of scheduling policies introduced for stochastic scheduling and which can be represented by a directed acyclic graph. We present a formal treatment of resource flows as a representation of resource-allocation decisions, extending the existing literature. A number of complexity results are established, showing that a number of recently proposed objective functions for evaluating the quality of ES-policies lead to difficult problems. Finally, some reflections are provided on possible efficiency enhancements to enumeration algorithms for ES-policies.

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Flow Improvement and Network Flows with Fixed Costs

Cited by 35 publications

References 8 publications

The minimum shift design problem

The minimum shift design problem

Sustainable Cloud Computing

An Investigation of Resource-Allocation Decisions by Means of Project Networks

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