Assignment Problems

Burkard, Rainer E.; Dell’Amico, Mauro; Martello, Silvano

doi:10.1137/1.9781611972238

Cited by 412 publications

(294 citation statements)

References 0 publications

Supporting

Mentioning

290

Contrasting

Unclassified

Order By: Relevance

“…This proves (6). From Theorem 2.5, we see that given a QAP with matrices (A, B) and a PSD matrix splitting (B 1 , B 2 ) of B, if the matrix splitting (B 1 , B 2 ) is redundant, then we have…”

Section: Redundant and Non-redundant Matrix Splittingmentioning

confidence: 63%

Semi-definite programming relaxation of quadratic assignment problems based on nonredundant matrix splitting

et al. 2014

View full text Add to dashboard Cite

Quadratic Assignment Problems (QAPs) are known to be among the most challenging discrete optimization problems. Recently, a new class of semi-definite relaxation (SDR) models for QAPs based on matrix splitting has been proposed [25,28]. In this paper, we consider the issue of how to choose an appropriate matrix splitting scheme so that the resulting relaxation model is easy to solve and able to provide a strong bound. For this, we first introduce a new notion of the so-called redundant and non-redundant matrix splitting and show that the relaxation based on a non-redundant matrix splitting can provide a stronger bound than a redundant one. Then we propose to follow the minimal trace principle to find a non-redundant matrix splitting via solving an auxiliary semi-definite programming problem (SDP). We show that applying the minimal trace principle directly leads to the so-called orthogonal matrix splitting introduced in [28]. To find other non-redundant matrix splitting schemes whose resulting relaxation models are relatively easy to solve, we elaborate on two splitting schemes based on the so-called one-matrix and the sum-matrix. We analyze the solutions from the auxiliary problems for these two cases and characterize when they can provide a non-redundant matrix splitting. The lower bounds from these two splitting schemes are compared theoretically. Promising numerical results on some large QAP instances are reported, which further validate our theoretical conclusions.

show abstract

Section: Redundant and Non-redundant Matrix Splittingmentioning

confidence: 63%

Semi-definite programming relaxation of quadratic assignment problems based on nonredundant matrix splitting

et al. 2014

View full text Add to dashboard Cite

show abstract

“…This problem can be recast as a linear sum assignment problem and solved in many different ways [4]. In practice, we use the Hungarian algorithm which is very fast for small assignment problems [3] (in our setting up to images with N = 256 2 pixels).…”

Section: Optimal Patch Assignmentmentioning

confidence: 99%

Optimal Patch Assignment for Statistically Constrained Texture Synthesis

Gutiérrez

Rabin

Galerne

et al. 2017

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. This article introduces a new model for patch-based texture synthesis that controls the distribution of patches in the synthesized texture. The proposed approach relies on an optimal assignment of patches over decimated pixel grids. This assignment problem formulates the synthesis as the minimization of a discrepancy measure between input's and output's patches through their optimal permutation. The resulting nonconvex optimization problem is addressed with an iterative algorithm alternating between a patch assignment step and a patch aggregation step. We show that this model statistically constrains the output texture content, while inheriting the structure-preserving property of patch-based methods. We also propose a relaxed patch assignment extension that increases the robustness to non-stationnary textures.

show abstract

“…Any late bids are stored for the evaluation during the next round of bids. The server converts the replica placement problem to a task assignment problem [9]. We calculate the profit of allocating the resources of a seller peer to every available buyer.…”

Section: Players Designmentioning

confidence: 99%

“…The goal is to reduce consumption of the bandwidth of all different peers while reducing the load on the storage servers. We started experimenting using the Hungarian algorithm [9] which proved not suitable because of its complexity O(n 4 ). We designed a greedy suboptimal task assignment engine that has lower complexity of O(n log n) where n is the number of peers.…”

Section: The Profit Functionmentioning

confidence: 99%