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112
Stochastic Load Balancing and Related Problems
 In FOCS
, 1999
"... We study the problems of makespan minimization (load balancing), knapsack, and bin packing when the jobs have stochastic processing requirements or sizes. If the jobs are all Poisson, we present a two approximation for the first problem using Graham's rule, and observe that polynomial time appr ..."
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Cited by 55 (4 self)
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We study the problems of makespan minimization (load balancing), knapsack, and bin packing when the jobs have stochastic processing requirements or sizes. If the jobs are all Poisson, we present a two approximation for the first problem using Graham's rule, and observe that polynomial time approximation schemes can be obtained for the last two problems. If the jobs are all exponential, we present polynomial time approximation schemes for all three problems. We also obtain quasipolynomial time approximation schemes for the last two problems if the jobs are Bernoulli variables. 1 Introduction In traditional scheduling problems, each job has a known deterministic size and duration. There are cases, however, where the exact size of a job is not known at the time when a scheduling decision needs to be made; all that is known is a probability distribution on the size of the job. Given a schedule, the value of the objective function itself becomes a random variable. The goal then is to find...
Maximizing Submodular Set Functions Subject to Multiple Linear Constraints
, 2009
"... The concept of submodularity plays a vital role in combinatorial optimization. In particular, many important optimization problems can be cast as submodular maximization problems, including maximum coverage, maximum facility location and max cut in directed/undirected graphs. In this paper we presen ..."
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Cited by 51 (1 self)
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The concept of submodularity plays a vital role in combinatorial optimization. In particular, many important optimization problems can be cast as submodular maximization problems, including maximum coverage, maximum facility location and max cut in directed/undirected graphs. In this paper we present the first known approximation algorithms for the problem of maximizing a nondecreasing submodular set function subject to multiple linear constraints. Given a ddimensional budget vector ¯ L, for some d ≥ 1, and an oracle for a nondecreasing submodular set function f over a universe U, where each element e ∈ U is associated with a ddimensional cost vector, we seek a subset of elements S ⊆ U whose total cost is at most ¯ L, such that f(S) is maximized. We develop a framework for maximizing submodular functions subject to d linear constraints that yields a (1 − ε)(1 − e−1)approximation to the optimum for any ε> 0, where d> 1 is some constant. Our study is motivated by a variant of the classical maximum coverage problem that we call maximum coverage with multiple packing constraints. We use our framework to obtain the same approximation ratio for this problem. To the best of our knowledge, this is the first time the theoretical bound of 1 − e−1 is (almost) matched for both of these problems.
Parameterized Complexity for the Skeptic
 In Proc. 18th IEEE Annual Conference on Computational Complexity
, 2003
"... The goal of this article is to provide a tourist guide, with an eye towards structural issues, to what I consider some of the major highlights of parameterized complexity. ..."
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Cited by 41 (1 self)
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The goal of this article is to provide a tourist guide, with an eye towards structural issues, to what I consider some of the major highlights of parameterized complexity.
Optimal Configuration for BGP Route Selection
 In Proc. IEEE INFOCOM
, 2003
"... An Internet Service Provider must provide transit service for traffic between its customers and its providers and, at the same time, attempt to minimize network utilization and balance traffic according to the capacities of its border routers. Central to the selection of border routers for transit t ..."
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Cited by 38 (0 self)
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An Internet Service Provider must provide transit service for traffic between its customers and its providers and, at the same time, attempt to minimize network utilization and balance traffic according to the capacities of its border routers. Central to the selection of border routers for transit traffic flows is the Border Gateway Protocol (BGP) between Autonomous Systems peers, through which route advertisements for network prefixes determine the selection of border routers for each traffic flow.
Dependent Rounding in Bipartite Graphs
"... We combine the pipage rounding technique of Ageev &Sviridenko with a recent rounding method developed by Srinivasan, to develop a new randomized rounding approachfor fractional vectors defined on the edgesets of bipartite graphs. We show various ways of combining this techniquewith other idea ..."
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Cited by 35 (5 self)
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We combine the pipage rounding technique of Ageev &Sviridenko with a recent rounding method developed by Srinivasan, to develop a new randomized rounding approachfor fractional vectors defined on the edgesets of bipartite graphs. We show various ways of combining this techniquewith other ideas, leading to the following applications: ffl richer randomgraph models for graphs with a givendegreesequence; ffl improved approximation algorithms for: (i) throughputmaximization in broadcast scheduling, (ii) delayminimization in broadcast scheduling, and (iii) capacitated vertex cover;
Polynomial Time Approximation Schemes for ClassConstrained Packing Problems
 Proc. of Workshop on Approximation Algorithms
, 1999
"... . We consider variants of the classic bin packing and multiple knapsack problems, in which sets of items of different classes (colors) need to be placed in bins; the items may have different sizes and values. Each bin has a limited capacity, and a bound on the number of distinct classes of items ..."
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Cited by 33 (6 self)
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. We consider variants of the classic bin packing and multiple knapsack problems, in which sets of items of different classes (colors) need to be placed in bins; the items may have different sizes and values. Each bin has a limited capacity, and a bound on the number of distinct classes of items it can hold. In the classconstrained multiple knapsack (CCMK) problem, our goal is to maximize the total value of packed items, whereas in the classconstrained binpacking (CCBP), we seek to minimize the number of (identical) bins, needed for packing all the items. We give a polynomial time approximation scheme (PTAS) for CCMK and a dual PTAS for CCBP. We also show that the 01 classconstrained knapsack admits a fully polynomial time approximation scheme, even when the number of distinct colors of items depends on the input size. Finally, we introduce the generalized classconstrained packing problem (GCCP), where each item may have more than one color. We show that GCCP is APX...
The Load Rebalancing Problem
 In Proc. of the 15th Ann. ACM Symp. on Parallel Algorithms and Architectures
, 2003
"... In the classical load balancing or multiprocessor scheduling problem, we are given a sequence of jobs of varying sizes and are asked to assign each job to one of the m empty processors. A typical objective is to minimize makespan, the load on the heaviest loaded processor. Since in most real world ..."
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Cited by 33 (0 self)
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In the classical load balancing or multiprocessor scheduling problem, we are given a sequence of jobs of varying sizes and are asked to assign each job to one of the m empty processors. A typical objective is to minimize makespan, the load on the heaviest loaded processor. Since in most real world scenarios the load is a dynamic measure, the initial assignment may be not remain optimal with time. Motivated by such considerations in a variety of systems, we formulate the problem of load rebalancing — given a possibly suboptimal assignment of jobs to processors, relocate a set of the jobs so as to decrease the makespan. Specifically, the goal is to achieve the best possible makespan under the constraint that no more than k jobs are relocated. We also consider a generalization of this problem where there is an arbitrary cost function associated with each job relocation. Since the problem is clearly NPhard, we focus on approximation algorithms. We construct a sophisticated algorithm which achieves a 1.5approximation, with near linear running time. We also show that the problem has a PTAS, resolving the complexity issue. Finally, we investigate the approximability of several extensions of the rebalancing model.
An efficient approximation for the generalized assignment problem
 Information Processing Letters
, 2006
"... We present a simple family of algorithms for solving the Generalized Assignment Problem (GAP). Our technique is based on a novel combinatorial translation of any algorithm for the knapsack problem into an approximation algorithm for GAP. If the approximation ratio of the knapsack algorithm is α and ..."
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Cited by 33 (6 self)
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We present a simple family of algorithms for solving the Generalized Assignment Problem (GAP). Our technique is based on a novel combinatorial translation of any algorithm for the knapsack problem into an approximation algorithm for GAP. If the approximation ratio of the knapsack algorithm is α and its running time is O(f(N)), our algorithm guarantees a (1 + α) approximation ratio, and it runs in O(M · f(N) + M · N), where N is the number of items and M is the number of bins. Not only does our technique comprise a general interesting framework for the GAP problem; it also matches the best combinatorial approximation for this problem, with a much simpler algorithm and a better running time.
Scheduling algorithms for multicarrier wireless data systems
 IEEE/ACM Trans. Networking
, 2011
"... ..."
Dynamic resource allocation for spot markets in clouds
 in Proc. HOTICE
, 2011
"... Cloud computing promises ondemand provisioning of resource to applications and services. To deal with dynamically fluctuating resource demands, marketdriven resource allocation has been proposed and recently implemented by commercial cloud providers like Amazon EC2. In this environment, cloud reso ..."
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Cited by 27 (0 self)
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Cloud computing promises ondemand provisioning of resource to applications and services. To deal with dynamically fluctuating resource demands, marketdriven resource allocation has been proposed and recently implemented by commercial cloud providers like Amazon EC2. In this environment, cloud resources are offered in distinct types of virtual machines (VMs) and the cloud provider runs a continuous marketdriven mechanism for each VM type with the goal of achieving maximum revenue over time. However, as demand of each VM type can fluctuate independently at run time, it becomes a challenging problem to dynamically allocate data center resources to each spot market to maximize cloud provider’s total revenue. In this paper, we present a solution to this problem that consists of 2 parts: (1) market analysis for forecasting the demand for each spot market, and (2) a dynamic scheduling and consolidation mechanism that allocate resource to each spot market to maximize total revenue. As optimally allocating resources for revenue maximization is a NPhard problem, we show our algorithms can approximate the optimal solutions to this problem under both fixed and variable pricing schemes. Simulation studies confirm the effectiveness of our approach. 1