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46
Auction algorithms for network flow problems: A tutorial introduction
 Comput. Optim. Appl
, 1992
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New scaling algorithms for the assignment and minimum mean cycle problems
, 1992
"... In this paper we suggest new scaling algorithms for the assignment and minimum mean cycle problems. Our assignment algorithm is based on applying scaling to a hybrid version of the recent auction algorithm of Bertsekas and the successive shortest path algorithm. The algorithm proceeds by relaxing th ..."
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Cited by 47 (4 self)
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In this paper we suggest new scaling algorithms for the assignment and minimum mean cycle problems. Our assignment algorithm is based on applying scaling to a hybrid version of the recent auction algorithm of Bertsekas and the successive shortest path algorithm. The algorithm proceeds by relaxing the optimality conditions, and the amount of relaxation is successively reduced to zero. On a network with 2n nodes, m arcs, and integer arc costs bounded by C, the algorithm runs in O(,/n m log(nC)) time and uses very simple data structures. This time bound is comparable to the time taken by Gabow and Tarjan's scaling algorithm, and is better than all other time bounds under the similarity assumption, i.e., C = O(n k) for some k. We next consider the minimum mean cycle problem. The mean cost of a cycle is defined as the cost of the cycle divided by the number of arcs it contains. The minimum mean cycle problem is to identify a cycle whose mean cost is minimum. We show that by using ideas of the assignment algorithm in an approximate binary search procedure, the minimum mean cycle problem can also be solved in O(~/n m log nC) time. Under the similarity assumption, this is the best available time bound to solve the minimum mean cycle problem.
Linear Assignment Problems and Extensions
"... This paper aims at describing the state of the art on linear assignment problems (LAPs). Besides sum LAPs it discusses also problems with other objective functions like the bottleneck LAP, the lexicographic LAP, and the more general algebraic LAP. We consider different aspects of assignment problems ..."
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Cited by 41 (0 self)
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This paper aims at describing the state of the art on linear assignment problems (LAPs). Besides sum LAPs it discusses also problems with other objective functions like the bottleneck LAP, the lexicographic LAP, and the more general algebraic LAP. We consider different aspects of assignment problems, starting with the assignment polytope and the relationship between assignment and matching problems, and focusing then on deterministic and randomized algorithms, parallel approaches, and the asymptotic behaviour. Further, we describe different applications of assignment problems, ranging from the well know personnel assignment or assignment of jobs to parallel machines, to less known applications, e.g. tracking of moving objects in the space. Finally, planar and axial threedimensional assignment problems are considered, and polyhedral results, as well as algorithms for these problems or their special cases are discussed. The paper will appear in the Handbook of Combinatorial Optimization to be published
An Efficient Cost Scaling Algorithm for the Assignment Problem
 MATH. PROGRAM
, 1995
"... The cost scaling pushrelabel method has been shown to be efficient for solving minimumcost flow problems. In this paper we apply the method to the assignment problem and investigate implementations of the method that take advantage of assignment's special structure. The results show that the metho ..."
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Cited by 36 (1 self)
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The cost scaling pushrelabel method has been shown to be efficient for solving minimumcost flow problems. In this paper we apply the method to the assignment problem and investigate implementations of the method that take advantage of assignment's special structure. The results show that the method is very promising for practical use.
User Profile Replication for Faster Location Lookup in Mobile Environments
, 1995
"... We consider peruser profile replication as a mechanism for faster location lookup of mobile users in a Personal Communications Service system. We present a minimumcost maximumflow based algorithm to compute the set of sites at which a user profile should be replicated given known calling and user ..."
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Cited by 35 (0 self)
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We consider peruser profile replication as a mechanism for faster location lookup of mobile users in a Personal Communications Service system. We present a minimumcost maximumflow based algorithm to compute the set of sites at which a user profile should be replicated given known calling and user mobility patterns. We then present schemes for replication plans that gracefully adapt to changes in the calling and mobility patterns. 1 Introduction In a Personal Communications Service (PCS) system, users place and receive calls through a wireless medium. Calls may deliver voice, data, text, facsimile, or video information [JLLM94]. PCS users are located in systemdefined cells, which are bounded geographical areas. When a user places a call, the PCS infrastructure must route the call to the basestation located in the same cell as the callee. The basestation then transmits the data in the call to the PCS unit through the wireless medium. We consider the problem of locating users who...
DUAL COORDINATE STEP METHODS FOR LINEAR NETWORK FLOW PROBLEMS
, 1988
"... We review a class of recentlyproposed linearcost network flow methods which are amenable to distributed implementation. All the methods in the class use the notion of ecomplementary slackness, and most do not explicitly manipulate any "global " objects such as paths, trees, or cuts. Interestingly ..."
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Cited by 29 (7 self)
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We review a class of recentlyproposed linearcost network flow methods which are amenable to distributed implementation. All the methods in the class use the notion of ecomplementary slackness, and most do not explicitly manipulate any "global " objects such as paths, trees, or cuts. Interestingly, these methods have stimulated a large number of new serial computational complexity results. We develop the basic theory of these methods and present two specific methods, the erelaxation algorithm for the minimumcost flow problem, and the auction algorithm for the assignment problem. We show how to implement these methods with serial complexities of O(N 3 log NC) and O(NA log NC), respectively. We also discuss practical implementation issues and computational experience to date. Finally, we show how to implement erelaxation in a completely asynchronous, "chaotic" environment in which some processors compute faster than others, some processors communicate faster than others, and there can be arbitrarily large communication delays.
PerUser Profile Replication in Mobile Environments: Algorithms, Analysis, and Simulation Results
 Journal on Special Topics in Mobile Networks and Applications, special issue on Data Management
, 1997
"... We consider peruser profile replication as a mechanism for faster location lookup of mobile users in a Personal Communications Service system. We present a minimumcost maximumflow based algorithm to compute the set of sites at which a user profile should be replicated given known calling and user ..."
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Cited by 25 (1 self)
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We consider peruser profile replication as a mechanism for faster location lookup of mobile users in a Personal Communications Service system. We present a minimumcost maximumflow based algorithm to compute the set of sites at which a user profile should be replicated given known calling and user mobility patterns. We then present schemes for replication plans that gracefully adapt to changes in the calling and mobility patterns. We show the costs and benefits of our replication algorithm against previous location lookup approaches through analysis. We also simulate our algorithm against other location lookup algorithms on a realistic model of a geographical area to evaluate critical system performance measures. A notable aspect of our simulations is that we use wellvalidated models of user calling and mobility patterns. 1 Introduction In a Personal Communications Service (PCS) system, users place and receive calls through a wireless medium. Calls may deliver voice, data, text, fa...
Price Prediction Strategies for MarketBased Scheduling
 To appear, Fourteenth International Conference on Automated Planning and Scheduling
, 2004
"... In a marketbased scheduling mechanism, the allocation of timespecific resources to tasks is governed by a competitive bidding process. Agents bidding for multiple, separately allocated time slots face the risk that they will succeed in obtaining only part of their requirement, incurring expenses f ..."
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Cited by 18 (6 self)
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In a marketbased scheduling mechanism, the allocation of timespecific resources to tasks is governed by a competitive bidding process. Agents bidding for multiple, separately allocated time slots face the risk that they will succeed in obtaining only part of their requirement, incurring expenses for potentially worthless slots. We investigate the use of price prediction strategies to manage such risk. Given an uncertain price forecast, agents follow simple rules for choosing whether and on which time slots to bid. We find that employing price predictions can indeed improve performance over a straightforward baseline in some settings. Using an empirical gametheoretic methodology, we establish Nash equilibrium profiles for restricted strategy sets. This allows us to confirm the stability of pricepredicting strategies, and measure overall efficiency. We further experiment with variant strategies to analyze the source of prediction’s power, demonstrate the existence of selfconfirming predictions, and compare the performance of alternative prediction methods.
On Combinatorial Auction and Lagrangean Relaxation for Distributed Resource Scheduling
 IIE Transactions
, 1998
"... Most existing methods for scheduling are based on centralized or hierarchical decision making using monolithic models. In this study, we investigate a new method based on a distributed and locally autonomous decision structure using the notion of combinatorial auction. In combinatorial auction the b ..."
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Cited by 18 (4 self)
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Most existing methods for scheduling are based on centralized or hierarchical decision making using monolithic models. In this study, we investigate a new method based on a distributed and locally autonomous decision structure using the notion of combinatorial auction. In combinatorial auction the bidders demand a combination of dependent objects with a single bid. We show that not only can we use this auction mechanism to handle complex resource scheduling problems, but there exist strong links between combinatorial auction and Lagrangeanbased decomposition. Exploring some of these properties, we characterize combinatorial auction using auction protocols and payment functions. This study is a #rst step toward developing a distributed scheduling framework that maintains systemwide performance while accommodating local preferences and objectives. We provide some insights to this framework by demonstrating four di#erent versions of the auction mechanism using job shop scheduling proble...