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348
Ratedistortion methods for image and video compression
 IEEE Signal Process. Mag. 1998
"... In this paper we provide an overview of ratedistortion (RD) based optimization techniques and their practical application to image and video coding. We begin with a short discussion of classical ratedistortion theory and then we show how in many practical coding scenarios, such as in standardsco ..."
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Cited by 222 (7 self)
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In this paper we provide an overview of ratedistortion (RD) based optimization techniques and their practical application to image and video coding. We begin with a short discussion of classical ratedistortion theory and then we show how in many practical coding scenarios, such as in standardscompliant coding environments, resource allocation can be put in an RD framework. We then introduce two popular techniques for resource allocation, namely, Lagrangian optimization and dynamic programming. After a discussion of these two techniques as well as some of their extensions, we conclude with a quick review of recent literature in these areas citing a number of applications related to image and video compression and transmission. We
An Empirical Study of Algorithms for Point Feature Label Placement
, 1994
"... A major factor affecting the clarity of graphical displays that include text labels is the degree to which labels obscure display features (including other labels) as a result of spatial overlap. Pointfeature label placement (PFLP) is the problem of placing text labels adjacent to point features on ..."
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Cited by 162 (8 self)
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A major factor affecting the clarity of graphical displays that include text labels is the degree to which labels obscure display features (including other labels) as a result of spatial overlap. Pointfeature label placement (PFLP) is the problem of placing text labels adjacent to point features on a map or diagram so as to maximize legibility. This problem occurs frequently in the production of many types of informational graphics, though it arises most often in automated cartography. In this paper we present a comprehensive treatment of the PFLP problem, viewed as a type of combinatorial optimization problem. Complexity analysis reveals that the basic PFLP problem and most interesting variants of it are NPhard. These negative results help inform a survey of previously reported algorithms for PFLP; not surprisingly, all such algorithms either have exponential time complexity or are incomplete. To solve the PFLP problem in practice, then, we must rely on good heuristic methods. We pr...
A Heuristic Method for the Set Covering Problem
 OPERATIONS RESEARCH
, 1995
"... We present a Lagrangianbased heuristic for the wellknown Set Covering Problem (SCP). The algorithm was initially designed for solving very large scale SCP instances, involving up to 5,000 rows and 1,000,000 columns, arising from crew scheduling in the Italian Railway Company, Ferrovie dello St ..."
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Cited by 91 (13 self)
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We present a Lagrangianbased heuristic for the wellknown Set Covering Problem (SCP). The algorithm was initially designed for solving very large scale SCP instances, involving up to 5,000 rows and 1,000,000 columns, arising from crew scheduling in the Italian Railway Company, Ferrovie dello Stato SpA. In 1994 Ferrovie dello Stato SpA, jointly with the Italian Operational Research Society, organized a competition, called FASTER, intended to promote the development of algorithms capable of producing good solutions for these instances, since the classical approaches meet with considerable difficulties in tackling them. The main characteristics of the algorithm we propose are (1) a dynamic pricing scheme for the variables, akin to that used for solving largescale LP's, to be coupled with subgradient optimization and greedy algorithms, and (2) the systematic use of column fixing to obtain improved solutions. Moreover, we propose a number of improvements on the standard way o...
Convex Nondifferentiable Optimization: A Survey Focussed On The Analytic Center Cutting Plane Method.
, 1999
"... We present a survey of nondifferentiable optimization problems and methods with special focus on the analytic center cutting plane method. We propose a selfcontained convergence analysis, that uses the formalism of the theory of selfconcordant functions, but for the main results, we give direct pr ..."
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Cited by 76 (2 self)
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We present a survey of nondifferentiable optimization problems and methods with special focus on the analytic center cutting plane method. We propose a selfcontained convergence analysis, that uses the formalism of the theory of selfconcordant functions, but for the main results, we give direct proofs based on the properties of the logarithmic function. We also provide an in depth analysis of two extensions that are very relevant to practical problems: the case of multiple cuts and the case of deep cuts. We further examine extensions to problems including feasible sets partially described by an explicit barrier function, and to the case of nonlinear cuts. Finally, we review several implementation issues and discuss some applications.
A Minimal Algorithm for the MultipleChoice Knapsack Problem.
 European Journal of Operational Research
, 1994
"... The MultipleChoice Knapsack Problem is defined as a 01 Knapsack Problem with the addition of disjoined multiplechoice constraints. As for other knapsack problems most of the computational effort in the solution of these problems is used for sorting and reduction. But although O(n) algorithms whic ..."
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Cited by 55 (4 self)
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The MultipleChoice Knapsack Problem is defined as a 01 Knapsack Problem with the addition of disjoined multiplechoice constraints. As for other knapsack problems most of the computational effort in the solution of these problems is used for sorting and reduction. But although O(n) algorithms which solves the linear MultipleChoice Knapsack Problem without sorting have been known for more than a decade, such techniques have not been used in enumerative algorithms.
Analyzing and Exploiting the Structure of the Constraints in the ILP Approach to the Scheduling Problem
 IEEE Transactions on VLSI Systems
, 1994
"... In integer linear programming (ILP), formulating a "good" model is of crucial importance to solving that model [1]. In this paper, we begin with a mathematical analysis of the structure of the assignment, timing, and resource constraints in highlevel synthesis, and then evaluate the struc ..."
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Cited by 52 (9 self)
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In integer linear programming (ILP), formulating a "good" model is of crucial importance to solving that model [1]. In this paper, we begin with a mathematical analysis of the structure of the assignment, timing, and resource constraints in highlevel synthesis, and then evaluate the structure of the scheduling polytope described by these constraints. We then show how the structure of the constraints can be exploited to develop a wellstructured ILP formulation, which can serve as a solid theoretical foundation for future improvement. As a start in that direction, we also present two methods to further tighten the formulation. The contribution of this paper is twofold: (1) it provides the first indepth formal analysis of the structure of the constraints, and it shows how to exploit that structure in a welldesigned ILP formulation, and (2) it shows how to further improve a wellstructured formulation by adding new valid inequalities. I. Introduction The scheduling problem in highle...
On Ascending Vickrey Auctions for Heterogeneous Objects
, 2005
"... We construct an ascending auction for heterogeneous objects by applying a primaldual algorithm to a linear program that represents the efficientallocation problem for this setting. The auction assigns personalized prices to bundles, and asks bidders to report their preferred bundles in each round. ..."
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Cited by 51 (4 self)
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We construct an ascending auction for heterogeneous objects by applying a primaldual algorithm to a linear program that represents the efficientallocation problem for this setting. The auction assigns personalized prices to bundles, and asks bidders to report their preferred bundles in each round. A bidder’s prices are increased when he belongs to a “minimally undersupplied ” set of bidders. This concept generalizes the notion of “overdemanded” sets of objects introduced by Demange et al. (1986) for the onetoone assignment problem. Under a submodularity condition, the auction implements the Vickrey–Clarke–Groves outcome; we show that this type of condition is somewhat necessary to do so. When classifying the ascendingauction literature in terms of their underlying algorithms, our auction fills a gap in that literature. We relate our results to various ascending auctions in the literature.
Reliability Models for Facility Location: The Expected Failure Cost Case
 Transportation Science
, 2004
"... Classical facility location models like the Pmedian problem (PMP) and the uncapacitated fixedcharge location problem (UFLP) implicitly assume that once constructed, the facilities chosen will always operate as planned. In reality, however, facilities "fail" from time to time due to poor ..."
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Cited by 47 (10 self)
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Classical facility location models like the Pmedian problem (PMP) and the uncapacitated fixedcharge location problem (UFLP) implicitly assume that once constructed, the facilities chosen will always operate as planned. In reality, however, facilities "fail" from time to time due to poor weather, labor actions, changes of ownership, or other factors. Such failures may lead to excessive transportation costs as customers must be served from facilities much farther than their regularly assigned facilities. In this paper, we present models for choosing facility locations to minimize cost while also taking into account the expected transportation cost after failures of facilities. The goal is to choose facility locations that are both inexpensive under traditional objective functions and also reliable. This reliability approach is new in the facility location literature. We formulate reliability models based on both the PMP and the UFLP and present an optimal Lagrangian relaxation algorithm to solve them. We discuss how to use these models to generate a tradeo# curve between the daytoday operating cost and the expected cost taking failures into account, and use these tradeo# curves to demonstrate empirically that substantial improvements in reliability are often possible with minimal increases in operating cost.