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116
Crowder: Crowdsourcing entity resolution
 PVLDB
, 2012
"... Entity resolution is central to data integration and data cleaning. Algorithmic approaches have been improving in quality, but remain far from perfect. Crowdsourcing platforms offer a more accurate but expensive (and slow) way to bring human insight into the process. Previous work has proposed batch ..."
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Cited by 14 (2 self)
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Entity resolution is central to data integration and data cleaning. Algorithmic approaches have been improving in quality, but remain far from perfect. Crowdsourcing platforms offer a more accurate but expensive (and slow) way to bring human insight into the process. Previous work has proposed batching verification tasks for presentation to human workers but even with batching, a humanonly approach is infeasible for data sets of even moderate size, due to the large numbers of matches to be tested. Instead, we propose a hybrid humanmachine approach in which machines are used to do an initial, coarse pass over all the data, and people are used to verify only the most likely matching pairs. Weshowthatforsuchahybridsystem, generatingthe minimum number of verification tasks of a given size is NPHard, but we develop a novel twotiered heuristic approach for creating batched tasks. We describe this method, and present the results of extensive experiments on real data sets using a popular crowdsourcing platform. The experiments show that our hybrid approach achieves both good efficiency and highaccuracy compared tomachineonlyor humanonly alternatives. 1.
Models and Algorithms for ThreeStage TwoDimensional Bin Packing
 INSTITUTE OF COMPUTER GRAPHICS AND ALGORITHMS, VIENNA UNIVERSITY OF TECHNOLOGY
, 2004
"... We consider the threestage twodimensional bin packing problem (2BP) which occurs in realworld applications such as glass, paper, or steel cutting. We present new integer linear programming formulations: Models for a restricted version and the original version of the problem are developed. Both in ..."
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Cited by 13 (5 self)
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We consider the threestage twodimensional bin packing problem (2BP) which occurs in realworld applications such as glass, paper, or steel cutting. We present new integer linear programming formulations: Models for a restricted version and the original version of the problem are developed. Both involve polynomial numbers of variables and constraints only and e#ectively avoid symmetries. Those models are solved using CPLEX. Furthermore, a branchandprice (B&P) algorithm is presented for a set covering formulation of the unrestricted problem. We consider stabilizing the column generation process of the B&P algorithm using dualoptimal inequalities. Fast column generation is performed by applying a hierarchy of four methods: (a) a fast greedy heuristic, (b) an evolutionary algorithm, (c) solving a restricted form of the pricing problem using CPLEX, and finally (d) solving the complete pricing problem using CPLEX. Computational experiments on standard benchmark instances document the benefits of the new approaches: The restricted version of the ILP model can be used for quickly obtaining nearly optimal solutions. The unrestricted version is computationally more expensive. Column generation provides a strong lower bound for 3stage 2BP. The combination of all four pricing algorithms and column generation stabilization in the proposed B&P framework yields the best results in terms of the average objective value, the average runtime, and the number of instances solved to proven optimality.
Integer Program Reformulation for Robust BranchandCutandPrice Algorithms
 In Proceedings of the Conference Mathematical Program in Rio: A Conference in Honour of Nelson Maculan
, 2003
"... Since cut and column generation were established as two of the most important techniques in integer programming, researchers have looked for ways of combining them into a robust branchandcutandprice algorithm. Here, "robust" means that neither branching nor the addition of cuts should ..."
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Cited by 11 (3 self)
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Since cut and column generation were established as two of the most important techniques in integer programming, researchers have looked for ways of combining them into a robust branchandcutandprice algorithm. Here, "robust" means that neither branching nor the addition of cuts should change the structure of the pricing subproblems. In the last few years, several researchers independently noted that cuts expressed in terms of variables from a suitable original formulation could be added to the master problem without disturbing the pricing. This fact is still little known outside the "column generation community" and its consequences on integer programming are just beginning to be explored. This work intends to be an analysis of how to reformulate an integer program in order to build an e#cient robust branchandcutand price. In particular, we propose an alternative master problem that can be quite advantageous in some situations. Another key issue addressed is how to avoid the pitfalls that arise from variable symmetries in the original formulations of many problems. We refer to extensive computational experiments on the capacitated vehicle routing, capacitated minimum spanning tree, and generalized assignment problems. Remarkable results on benchmark instances from the literature clearly attest the power of combining cut and column generation.
A Cutting Plane Algorithm for the OneDimensional Cutting Stock Problem with Multiple Stock Lengths
 European Journal of Operational Research
, 2002
"... . A cutting plane approach combining ChvatalGomory cutting planes with column generation is generalized for the case of multiple stock lengths in the onedimensional cutting stock problem. Appropriate modications of the column generation procedure and the rounding heuristic are proposed. A comparis ..."
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Cited by 9 (7 self)
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. A cutting plane approach combining ChvatalGomory cutting planes with column generation is generalized for the case of multiple stock lengths in the onedimensional cutting stock problem. Appropriate modications of the column generation procedure and the rounding heuristic are proposed. A comparison with the branchandprice method for the problem with one stock type and representative test results are reported. Keywords: cutting, cutting planes, column generation, heuristics, branchandbound 1
Families of NonIRUP instances of the onedimensional cutting stock problem
, 1998
"... In case of the onedimensional cutting stock problem (CSP) one can observe for any instance a very small gap between the integer optimal value and the continuous relaxation bound. These observations have initiated a series of investigations. An instance possesses the integer roundup property (IRUP) ..."
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Cited by 9 (6 self)
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In case of the onedimensional cutting stock problem (CSP) one can observe for any instance a very small gap between the integer optimal value and the continuous relaxation bound. These observations have initiated a series of investigations. An instance possesses the integer roundup property (IRUP) if its gap is smaller than 1. It is wellknown that there exist instances of the CSP having a gap greater than 1 but there is not known any instance with gap at least 2. In this paper we present families of nonIRUP instances and give methods to construct such instances. Furthermore, an equivalence relation for instances of the CSP is considered to become independent from the real size parameters.
Carathéodory bounds for integer cones
 OPERATIONS RESEARCH LETTERS, 34:564
, 2006
"... Let b ∈ Z d be an integer conic combination of a finite set of integer vectors X ⊂ Z d. In this note we provide upper bounds on the size of a smallest subset �X ⊆ X such that b is an integer conic combination of elements of �X. We apply our bounds to general integer programming and to the cutting st ..."
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Cited by 7 (0 self)
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Let b ∈ Z d be an integer conic combination of a finite set of integer vectors X ⊂ Z d. In this note we provide upper bounds on the size of a smallest subset �X ⊆ X such that b is an integer conic combination of elements of �X. We apply our bounds to general integer programming and to the cutting stock problem and provide an NP certificate for the latter, whose existence has not been known so far.
Solving onedimensional cutting stock problems exactly with a cutting plane algorithm
, 1999
"... ..."
Tighter relaxations for the cutting stock problem
 European Journal of Operational Research
, 1999
"... In the cutting stock problem (CSP) a given order for smaller pieces has to be cut from larger stock material in such a way that the number of stock material needed is minimal. Based on the classical integer linear programming model the common solution technique consists of solving the corresponding ..."
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Cited by 7 (5 self)
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In the cutting stock problem (CSP) a given order for smaller pieces has to be cut from larger stock material in such a way that the number of stock material needed is minimal. Based on the classical integer linear programming model the common solution technique consists of solving the corresponding continuous relaxation problem followed by several heuristics which construct integer solutions. In many cases an optimal solution can be obtained quickly in this way. But for instances which do not possess the integer roundup property the optimality of the solution obtained cannot be verified by means of the LP bound. In order to overcome this nonsatisfactory situation, two tighter relaxations of the CSP are proposed, and results of theoretical and numerical investigations are presented.
DantzigWolfe Decomposition and BranchandPrice Solving in G12
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"... The date of receipt and acceptance will be inserted by the editor Abstract The G12 project is developing a software environment for stating and solving combinatorial problems by mapping a highlevel model of the problem to an efficient combination of solving methods. Model annotations are used to co ..."
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Cited by 7 (0 self)
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The date of receipt and acceptance will be inserted by the editor Abstract The G12 project is developing a software environment for stating and solving combinatorial problems by mapping a highlevel model of the problem to an efficient combination of solving methods. Model annotations are used to control this process. In this paper we explain the mapping to branchandprice solving. DantzigWolfe decomposition is automatically performed using the additional information given by the model annotations. The obtained models can then be solved using column generation and branchandprice. G12 supports the selection of specialised subproblem solvers, the aggregation of identical subproblems to reduce symmetries, automatic disaggregation when required by branchandbound, the use of specialised subproblem constraintbranching rules, and different master problem solvers including a hybrid solver based on the volume algorithm. We demonstrate the benefits of the G12 framework on three examples: a trucking problem, cutting stock, and twodimensional bin packing.