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15
LPbased approximation algorithms for capacitated facility location
 in Proc. of IPCO’04, 2004
"... In the capacitated facility location problem with hard capacities, we are given a set of facilities, F, and a set of clients D in a common metric space. Each facility i has a facility opening cost fi and capacity ui that specifies the maximum number of clients that may be assigned to this facility. ..."
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Cited by 23 (1 self)
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In the capacitated facility location problem with hard capacities, we are given a set of facilities, F, and a set of clients D in a common metric space. Each facility i has a facility opening cost fi and capacity ui that specifies the maximum number of clients that may be assigned to this facility. We want to open some facilities from the set F and assign each client to an open facility so that at most ui clients are assigned to any open facility i. The cost of assigning client j to facility i is given by the distance cij, and our goal is to minimize the sum of the facility opening costs and the client assignment costs. The only known approximation algorithms that deliver solutions within a constant factor of optimal for this NPhard problem are based on local search techniques. It is an open problem to devise an approximation algorithm for this problem based on a linear programming lower bound (or indeed, to prove a constant integrality gap for any LP relaxation). We make progress on this question by giving a 5approximation algorithm for the special case in which all of the facility costs are equal, by rounding the optimal solution to the standard LP relaxation. One notable aspect of our algorithm is that it relies on partitioning the input into a collection of singledemand capacitated facility location problems, approximately solving them, and then combining these solutions in a natural way.
VDC Planner: Dynamic MigrationAware Virtual Data Center Embedding for Clouds
 Proc. of the IFIP/IEEE Integrated Network Management Symposium (IM). Ghent (Belgium
, 2013
"... Abstract—Cloud computing promises to provide computing resources to a large number of service applications in an ondemand manner. Traditionally, cloud providers such as Amazon only provide guaranteed allocation for compute and storage resources, and fails to support the bandwidth requirements and p ..."
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Cited by 5 (1 self)
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Abstract—Cloud computing promises to provide computing resources to a large number of service applications in an ondemand manner. Traditionally, cloud providers such as Amazon only provide guaranteed allocation for compute and storage resources, and fails to support the bandwidth requirements and performance isolation among these applications. To address this limitation, recently a number of proposals advocate providing both guaranteed server and network resources in the form of Virtual Data Centers (VDCs). This raises the problem of optimally allocating both servers resources and data center networks to multiple VDCs in order to optimize total revenue, while minimizing the total energy consumption in the data center. However, despite recent studies on this problem, none of the existing solutions have considered the possibility of using VM migration to dynamically adjust the resource allocation, in order to meet the fluctuating resource demand of VDCs. In this paper, we propose VDC Planner, a migrationaware dynamic virtual data center embedding framework that aims at achieving high revenue while minimizing the total energy cost overtime. Our framework supports various usage scenarios, including VDC embedding, VDC scaling as well as dynamic VDC consolidation. Through experiments using realistic workload traces, we show our proposed approach achieves both higher revenue and lower average scheduling delay compared to existing solutions in the literature. I.
Resource Allocation for Covering Time Varying Demands
"... Abstract. We consider the problem of allocating resources to satisfy demand requirements varying over time. The input specifies a demand for each timeslot. Each resource is specified by a starttime, endtime, an associated cost and a capacity. A feasible solution is a multiset of resources such tha ..."
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Abstract. We consider the problem of allocating resources to satisfy demand requirements varying over time. The input specifies a demand for each timeslot. Each resource is specified by a starttime, endtime, an associated cost and a capacity. A feasible solution is a multiset of resources such that at any point of time, the sum of the capacities offered by the resources is at least the demand requirement at that point of time. The goal is to minimize the total cost of the resources included in the solution. This problem arises naturally in many scenarios such as workforce management, sensor networks, cloud computing, energy management and distributed computing. We study this problem under the partial cover setting and the zeroone setting. In the former scenario, the input also includes a number k and the goal is to choose a minimum cost solution that satisfies the demand requirements of at least k timeslots. For this problem, we present a 16approximation algorithm; we show that there exist “wellstructured ” nearoptimal solutions and that such a solution can be found in polynomial time via dynamic programming. In the zeroone setting, a feasible solution is allowed to pick at most one copy of any resource. For this case, we present a 4approximation algorithm; our algorithm uses a novel LP relaxation involving flowcover inequalities. 1
The lasserre hierarchy in almost diagonal form
 CoRR
"... The Lasserre hierarchy is a systematic procedure for constructing a sequence of increasingly tight relaxations that capture the convex formulations used in the best available approximation algorithms for a wide variety of optimization problems. Despite the increasing interest, there are very few t ..."
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Cited by 2 (1 self)
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The Lasserre hierarchy is a systematic procedure for constructing a sequence of increasingly tight relaxations that capture the convex formulations used in the best available approximation algorithms for a wide variety of optimization problems. Despite the increasing interest, there are very few techniques for analyzing Lasserre integrality gaps. Satisfying the positive semidefinite requirement is one of the major hurdles to constructing Lasserre gap examples. We present a novel characterization of the Lasserre hierarchy based on moment matrices that differ from diagonal ones by matrices of rank one (almost diagonal form). We provide a modular recipe to obtain positive semidefinite feasibility conditions by iteratively diagonalizing rank one matrices. Using this, we prove strong lower bounds on integrality gaps of Lasserre hierarchy for two basic capacitated covering problems. For the minknapsack problem, we show that the integrality gap remains arbitrarily large even at level n − 1 of Lasserre hierarchy. For the minsum of tardy jobs scheduling problem, we show that the integrality gap is unbounded at level Ω( n) (even when the objective function is integrated as a constraint). These bounds are interesting on their own, since both problems admit FPTAS. 1
Approximation algorithms for the partition vertex cover problem
 In WALCOM, volume 7748 of LNCS
, 2013
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Edge Covering with Budget Constrains
, 2013
"... We study two related problems: the Maximum weight m ′edge cover (MWEC) problem and the Fixed cost minimum edge cover (FCEC) problem. In the MWEC problem, we are given an undirected simple graph G = (V, E) with integral vertex weights. The goal is to select a set U ⊆ V of maximum weight so that the ..."
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We study two related problems: the Maximum weight m ′edge cover (MWEC) problem and the Fixed cost minimum edge cover (FCEC) problem. In the MWEC problem, we are given an undirected simple graph G = (V, E) with integral vertex weights. The goal is to select a set U ⊆ V of maximum weight so that the number of edges with at least one endpoint in U is at most m ′. Goldschmidt and Hochbaum [7] show that the problem is NPhard and they give a 3approximation algorithm for the problem. We present an approximation algorithm that achieves a guarantee of 2, thereby improving the bound of 3 [7]. In the FCEC problem, we are given a vertex weighted graph, a bound k, and our goal is to find a subset of vertices U of total weight at least k such that the number of edges with at least one edges in in U is minimized. A 2(1 + ɛ)approximation for the problem follows from the work of Carnes and Shmoys [4]. We improve the approximation ratio by giving a 2approximation algorithm for the problem. Can we get better results using methods based on linear programming? We take a first step and show that the natural LP for FCEC has an
On set expansion problems and the Small Set expansion Conjecture
"... Abstract. We consider problems related to the The Small Set expansion conjecture (Small set Expansion Conjecture) [14]. In the MWEC problem, we are given an undirected simple graph G = (V,E) with integral vertex weights. The goal is to select a set U ⊆ V of maximum weight so that the number of edge ..."
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Abstract. We consider problems related to the The Small Set expansion conjecture (Small set Expansion Conjecture) [14]. In the MWEC problem, we are given an undirected simple graph G = (V,E) with integral vertex weights. The goal is to select a set U ⊆ V of maximum weight so that the number of edges with at least one endpoint in U is at most m′. Goldschmidt and Hochbaum [8] show that the problem is NPhard and they give a 3approximation algorithm for the problem. We present a polynomial time approximation algorithm with ratio 2 algorithm for, MWEC improving the bound of 3 of [8]. Interestingly, we show that a 2 − ǫ ratio for MWEC for any constant ǫ> 0 implies that the Small set Expansion Conjecture [14] fails. Thus under the Small set Expansion Conjecture, the ratio is for MWEC, is tight. To the best of our knowledge, this is the first time that the Small set Expansion Conjecture is shown to be related to breaking the threshold of some approximation problem. The 2 − ǫ inapproximability considerably improves the NPC result of [8]. In the FCEC problem, we are given a vertex weighted graph, a bound k, and our goal is to find a subset of vertices U of total weight at least k such that the number of edges with at least one endpoint in in U is minimized. The NPC result in [8] carries over to this problem as well. The best known ratio for the problem is 2(1+ ǫ) by Carnes and Shmoys [3]. We give a polynomial time ratio 2 approximation algorithm for FCEC improving [3] and
A Truthful Incentive Mechanism for Emergency Demand Response in Colocation Data Centers
"... Abstract—Data centers are key participants in demand response programs, including emergency demand response (EDR), where the grid coordinates large electricity consumers for demand reduction in emergency situations to prevent major economic losses. While existing literature concentrates on ownerop ..."
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Abstract—Data centers are key participants in demand response programs, including emergency demand response (EDR), where the grid coordinates large electricity consumers for demand reduction in emergency situations to prevent major economic losses. While existing literature concentrates on owneroperated data centers, this work studies EDR in multitenant colocation data centers where servers are owned and managed by individual tenants. EDR in colocation data centers is significantly more challenging, due to lack of incentives to reduce energy consumption by tenants who control their servers and are typically on fixed power contracts with the colocation operator. Consequently, to achieve demand reduction goals set by the EDR program, the operator has to rely on the highly expensive and/or environmentallyunfriendly onsite energy backup/generation. To reduce cost and environmental impact, an efficient incentive mechanism is therefore in need, motivating tenants ’ voluntary energy reduction in case of EDR. This work proposes a novel incentive mechanism, TruthDR, which leverages a reverse auction to provide monetary remuneration to tenants according to their agreed energy reduction. TruthDR is computationally efficient, truthful, and achieves 2approximation in colocationwide social cost. Tracedriven simulations verify the efficacy of the proposed auction mechanism. I.
Management, Ghent: Belgium (2013)" VDC Planner: Dynamic MigrationAware Virtual Data Center Embedding for Clouds
, 2013
"... Abstract—Cloud computing promises to provide computing resources to a large number of service applications in an ondemand manner. Traditionally, cloud providers such as Amazon only provide guaranteed allocation for compute and storage resources, and fails to support the bandwidth requirements and pe ..."
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Abstract—Cloud computing promises to provide computing resources to a large number of service applications in an ondemand manner. Traditionally, cloud providers such as Amazon only provide guaranteed allocation for compute and storage resources, and fails to support the bandwidth requirements and performance isolation among these applications. To address this limitation, recently a number of proposals advocate providing both guaranteed server and network resources in the form of Virtual Data Centers (VDCs). This raises the problem of optimally allocating both servers resources and data center networks to multiple VDCs in order to optimize total revenue, while minimizing the total energy consumption in the data center. However, despite recent studies on this problem, none of the existing solutions have considered the possibility of using VM migration to dynamically adjust the resource allocation, in order to meet the fluctuating resource demand of VDCs. In this paper, we propose VDC Planner, a migrationaware dynamic virtual data center embedding framework that aims at achieving high revenue while minimizing the total energy cost overtime. Our framework supports various usage scenarios, including VDC embedding, VDC scaling as well as dynamic VDC consolidation. Through experiments using realistic workload traces, we show our proposed approach achieves both higher revenue and lower average scheduling delay compared to existing solutions in the literature. I.