Showing papers on "Assignment problem published in 2009"

A Path Following Algorithm for the Graph Matching Problem

Abstract: We propose a convex-concave programming approach for the labeled weighted graph matching problem. The convex-concave programming formulation is obtained by rewriting the weighted graph matching problem as a least-square problem on the set of permutation matrices and relaxing it to two different optimization problems: a quadratic convex and a quadratic concave optimization problem on the set of doubly stochastic matrices. The concave relaxation has the same global minimum as the initial graph matching problem, but the search for its global minimum is also a hard combinatorial problem. We, therefore, construct an approximation of the concave problem solution by following a solution path of a convex-concave problem obtained by linear interpolation of the convex and concave formulations, starting from the convex relaxation. This method allows to easily integrate the information on graph label similarities into the optimization problem, and therefore, perform labeled weighted graph matching. The algorithm is compared with some of the best performing graph matching methods on four data sets: simulated graphs, QAPLib, retina vessel images, and handwritten Chinese characters. In all cases, the results are competitive with the state of the art.

Quadratic Assignment Problem.

Abstract: The quadratic assignment problem (QAP) was introduced by Koopmans and Beckmann in 1957 as a mathematical model for the location of a set of indivisible economical activities [113]. Consider the problem of allocating a set of facilities to a set of locations, with the cost being a function of the distance and flow between the facilities, plus costs associated with a facility being placed at a certain location. The objective is to assign each facility to a location such that the total cost is minimized. Specifically, we are given three n x n input matrices with real elements F = (f ij ), D = (d kl ) and B = (b ik ), where f ij is the flow between the facility i and facility j, d kl is the distance between the location k and location l, and b ik is the cost of placing facility i at location k. The Koopmans-Beckmann version of the QAP can be formulated as follows: Let n be the number of facilities and locations and denote by N the set N = {1, 2,..., n}.

Learning Graph Matching

Abstract: As a fundamental problem in pattern recognition, graph matching has applications in a variety of fields, from computer vision to computational biology. In graph matching, patterns are modeled as graphs and pattern recognition amounts to finding a correspondence between the nodes of different graphs. Many formulations of this problem can be cast in general as a quadratic assignment problem, where a linear term in the objective function encodes node compatibility and a quadratic term encodes edge compatibility. The main research focus in this theme is about designing efficient algorithms for approximately solving the quadratic assignment problem, since it is NP-hard. In this paper we turn our attention to a different question: how to estimate compatibility functions such that the solution of the resulting graph matching problem best matches the expected solution that a human would manually provide. We present a method for learning graph matching: the training examples are pairs of graphs and the 'labels' are matches between them. Our experimental results reveal that learning can substantially improve the performance of standard graph matching algorithms. In particular, we find that simple linear assignment with such a learning scheme outperforms Graduated Assignment with bistochastic normalisation, a state-of-the-art quadratic assignment relaxation algorithm.

Online Ad Assignment with Free Disposal

Abstract: We study an online weighted assignment problem with a set of fixed nodes corresponding to advertisers and online arrival of nodes corresponding to ad impressions. Advertiser a has a contract for n(a) impressions, and each impression has a set of weighted edges to advertisers. The problem is to assign the impressions online so that while each advertiser a gets n(a) impressions, the total weight of edges assigned is maximized. Our insight is that ad impressions allow for free disposal, that is, advertisers are indifferent to, or prefer being assigned more than n(a) impressions without changing the contract terms. This means that the value of an assignment only includes the n(a) highest-weighted items assigned to each node a. With free disposal, we provide an algorithm for this problem that achieves a competitive ratio of 1 ? 1/e against the offline optimum, and show that this is the best possible ratio. We use a primal/dual framework to derive our results, applying a novel exponentially-weighted dual update rule. Furthermore, our algorithm can be applied to a general set of assignment problems including the ad words problem as a special case, matching the previously known 1 ? 1/e competitive ratio.

Exploiting group symmetry in semidefinite programming relaxations of the quadratic assignment problem

Abstract: We consider semidefinite programming relaxations of the quadratic assignment problem, and show how to exploit group symmetry in the problem data. Thus we are able to compute the best known lower bounds for several instances of quadratic assignment problems from the problem library: (Burkard et al. in J Global Optim 10:291–403, 1997).

A patient assignment algorithm for home care services

Abstract: We consider the problem of assigning patients to nurses for home care services. The aim is to balance the workload of the nurses while avoiding long travels to visit the patients. We analyse the case of the CSSS Cote-des-Neiges, Metro and Parc Extension for which a previous analysis has shown that demand fluctuations may create work overload for the nursing staff. We propose a mixed integer programming model with some non-linear constraints and a non-linear objective which we solve using a Tabu Search algorithm. A simplification of the workload measure leads to a linear mixed integer program which we optimize using CPLEX.

Dynamic cell formation and the worker assignment problem: a new model

Abstract: In this paper a new model is developed to deal with a simultaneous dynamic cell formation and worker assignment problem (SDCWP). Part routing flexibility and machine flexibility and also promotion of workers from one skill level to another are considered. The proposed model is formulated as a single objective nonlinear integer programming which is converted to a linear one. The objective function consists of two separate components. The first part of the objective function is related to machine-based costs such as production cost, intercell material handling cost, machine costs in the planning horizon. The second part is related to human issues and consists of hiring cost, firing cost, training cost and salary. It is the first time that worker assignment and dynamic cell formation are considered simultaneously. To verify the performance of the proposed model, some numerical examples are presented. Computational and sensitivity analysis results imply the significance of SDCWP.

Tracking a large number of objects from multiple views

Abstract: We propose a multi-object multi-camera framework for tracking large numbers of tightly-spaced objects that rapidly move in three dimensions. We formulate the problem of finding correspondences across multiple views as a multidimensional assignment problem and use a greedy randomized adaptive search procedure to solve this NP-hard problem efficiently. To account for occlusions, we relax the one-to-one constraint that one measurement corresponds to one object and iteratively solve the relaxed assignment problem. After correspondences are established, object trajectories are estimated by stereoscopic reconstruction using an epipolar-neighborhood search. We embedded our method into a tracker-to-tracker multi-view fusion system that not only obtains the three-dimensional trajectories of closely-moving objects but also accurately settles track uncertainties that could not be resolved from single views due to occlusion. We conducted experiments to validate our greedy assignment procedure and our technique to recover from occlusions. We successfully track hundreds of flying bats and provide an analysis of their group behavior based on 150 reconstructed 3D trajectories.

Lifting Based Wavelet Transforms on Graphs

Abstract: We present a novel method to implement lifting based wavelet transforms on general graphs. The detail and approximation coefficients computed from this graph transform can be interpreted similarly to their counterparts in standard signal processing process. Our approach is based on partitioning all nodes in the graph into two sets, containing "even" and "odd" nodes, respectively. Then, as in standard lifting, nodes of one parity are used to predict/update those of the other. We discuss the even-odd assignment problem on the graph and provide a solution that is well suited to construct the transform. As an example we discuss how our transform could be used in a denoising application. I. I NTRODUCTION

A channel and rate assignment algorithm and a layer-2.5 forwarding paradigm for multi-radio wireless mesh networks

Abstract: The availability of cost-effective wireless network interface cards makes it practical to design network devices with multiple radios which can be exploited to simultane-ously transmit/receive over different frequency channels. It has been shown that using multiple radios per node increases the throughput of multi-hop wireless mesh networks. However, multi-radios create several research challenges. A fundamental problem is the joint channel assignment and routing problem, i.e., how the channels can be assigned to radios and how a set of flow rates can be determined for every network link in order to achieve an anticipated objective. This joint problem is NP-com-plete. Thus, an approximate solution is developed by solving the channel assignment and the routing problems separately. The channel assignment problem turns out to be the problem to assign channels such that a given set of flow rates are schedulable and itself is shown to be also NP-complete. This paper shows that not only the channels but also the transmission rates of the links have to be properly selected to make a given set of flow rates schedulable. Thus, a greedy heuristic for the channel and rate assignment problem is developed. Algorithms to schedule the resulting set of flow rates have been proposed in the literature, which require synchronization among nodes and hence modified coordination functions. Unlike previous work, in this paper a forwarding paradigm is developed to achieve the resulting set of flow rates while using a standard MAC. A bi-dimensional Markov chain model of the proposed forwarding paradigm is presented to analyze its behavior. Thorough performance studies are con-ducted to: a) compare the proposed greedy heuristic to other channel assignment algorithms; b) analyze the behavior of the forwarding paradigm through numerical simulations based on the Markov chain model; c) simulate the operations of the forwarding paradigm and evaluate the achieved network throughput.

Cooperative Task Assignment/Path Planning of Multiple Unmanned Aerial Vehicles Using Genetic Algorithms

Abstract: This research was supported by the Korea Aerospace Research Institute for a program of development of the Communications, Navigation, Surveillance/Air Traffic Management system for the next generation.

Equivalent gap function-based reformulation and solution algorithm for the dynamic user equilibrium problem

Abstract: A variety of analytical and simulation-based models and algorithms have been developed for the dynamic user equilibrium (DUE) traffic assignment problem. This paper aims to develop a theoretically sound simulation-based DUE model and its solution algorithm, with particular emphasis on obtaining solutions that satisfy the DUE conditions. The DUE problem is reformulated, via a gap function, as a nonlinear minimization problem (NMP). The NMP is then solved by a column generation-based optimization procedure which embeds (i) a simulation-based dynamic network loading model to capture traffic dynamics and determine experienced path travel costs for a given path flow pattern and (ii) a path-swapping descent direction method to solve the restricted NMP defined by a subset of feasible paths. The descent direction method circumvents the need to compute the gradient of the objective function in finding search directions, or to determine suitable step sizes, which is especially valuable for large-scale simulation-based DUE applications. Computational results for both small and large real road networks confirm that the proposed formulation and solution algorithm are effective in obtaining near-optimal solutions to the DUE problem.

Monotonic Target Assignment for Robotic Networks

Abstract: Consider an equal number of mobile robotic agents and distinct target locations dispersed in an environment. Each agent has a limited communication range and either: 1) knowledge of every target position or 2) a finite-range sensor capable of acquiring target positions and no a priori knowledge of target positions. In this paper we study the following target assignment problem: design a distributed algorithm with which the agents divide the targets among themselves and, simultaneously, move to their unique target. We evaluate an algorithm's performance by characterizing its worst-case asymptotic time to complete the target assignment; that is the task completion time as the number of agents (and targets) increases, and the size of the environment scales to accommodate them. We introduce the intuitive class of monotonic algorithms, and give a lower bound on its worst-case completion time. We design and analyze two algorithms within this class: the ETSP Assgmt algorithm which works under assumption 1), and the Grid Assgmt algorithm which works under either assumption 1) or 2). In ldquosparse environments,rdquo where communication is infrequent, the ETSP Assgmt algorithm is within a constant factor of the optimal monotonic algorithm for worst-case initial conditions. In ldquodense environments,rdquo where communication is more prevalent, the Grid Assgmt algorithm is within a constant factor of the optimal monotonic algorithm for worst-case initial conditions. In addition we characterize the performance of the Grid Assgmt algorithm for uniformly distributed targets and agents, and for the case when there are more agents than targets.

Airline Fleet Assignment with Enhanced Revenue Modeling

Abstract: The airline fleet assignment problem addresses the question of how to best assign aircraft fleet types to scheduled flight legs. This paper presents the subnetwork fleet assignment model: a model that employs composite decision variables representing the simultaneous assignment of fleet types to subnetworks of one or more flight legs. The formulation is motivated by the need to better model the revenue side of the objective function. We present a solution method designed to balance revenue approximation and model tractability. Computational results suggest that the approach yields profit improvements over comparable models and that it is computationally tractable for problems of practical size.

Offline Impairment-Aware Routing and Wavelength Assignment Algorithms in Translucent WDM Optical Networks

Abstract: Physical impairments in optical fiber transmission necessitate the use of regeneration at certain intermediate nodes, at least for certain lengthy lightpaths. We design and implement impairment-aware algorithms for routing and wavelength assignment (IA-RWA) in translucent optical networks. We focus on the offline version of the problem, where we are given a network topology, the number of available wavelengths and a traffic matrix. The proposed algorithm selects the 3R regeneration sites and the number of regenerators that need to be deployed on these sites, solving the regenerator placement problem for the given set of requested connections. The problem can be also posed in a slightly different setting, where a (sparse) placement of regenerators in the network is given as input and the algorithm selects which of the available regenerators to use, solving the regenerator assignment problem. We formulate the problem of regenerator placement and regenerator assignment, as a virtual topology design problem, and address it using various algorithms, ranging from a series of integer linear programming (ILP) formulations to simple greedy heuristic algorithms. Once the sequence of regenerators to be used by the non-transparent connections has been determined, we transform the initial traffic matrix by replacing non-transparent connections with a sequence of transparent connections that terminate and begin at the specified 3R intermediate nodes. Using the transformed matrix we then apply an IA-RWA algorithm designed for transparent (as opposed to translucent) networks to route the traffic. Blocked connections are re-routed using any remaining regenerator(s) in the last phase of the algorithm.

Dynamic Task Scheduling with Load Balancing using Hybrid Particle Swarm Optimization

Abstract: This paper presents a Hybrid Particle Swarm Optimization (HPSO) method for solving the Task Assignment Problem (TAP) which is an np-hard problem. Particle Swarm Optimization (PSO) is a recently developed population based heuristic optimization technique. The algorithm has been developed to dynamically schedule heterogeneous tasks on to heterogeneous processors in a distributed setup. Load balancing which is a major issue in task scheduling is also considered. The nature of the tasks are independent and non pre-emptive. The HPSO yields a better result than the Normal PSO when applied to the task assignment problem. The results Of PSO and HPSO is also compared with another popular heuristic optimization technique namely Genetic Algorithm ( GA). The results infer that the PSO performs better than the GA.

Graph coloring based physical-cell-ID assignment for LTE networks

Abstract: Autoconfiguration of the radio parameters is a key feature for next generation mobile networks. Especially for LTE the NGMN Forum has brought it up as a major requirement. It is indispensable that algorithms used for autoconfiguration terminate quickly and do not cause infinite iterative reconfigurations within the network.Reference signal sequences are among the most important radio parameters for LTE, which are comparable to scrambling codes in 3G networks. In LTE they additionally serve as Cell Identifiers on the Physical Layer. Each cell is assigned one of the 504 available Physical Cell Identifiers. For proper operation the assignment has to be as well collision as also confusion free. Due to the high number and the layered structure of the cells within the network such as assignment is a complex task.In addition to this complexity each change of the Physical Cell ID of an operational cell causes a service interruption in the cell, which has to be avoided. The approach presented maps the ID assignment problem to the well known and well understood problem of graph coloring. It is shown that an efficient initial assignment even for complex networks is possible. Cells added during the subsequent network growth, can already be confused when inserted into the network. In this case the IDs of the operational cells causing the confusion must be changed.As a next logical step the incremental approach shows how the properties of the colored graph can be used for extending the network with new cells, with only minimal interruption while still retaining the properties of a colored graph.

Recommender systems for the conference paper assignment problem

Abstract: We present a recommender systems approach to conference paper assignment, i.e., the task of assigning paper submissions to reviewers. We address both the modeling of reviewer-paper preferences (which can be cast as a learning problem) and the optimization of reviewing assignments to satisfy global conference criteria (which can be viewed as constraint satisfaction). Due to the paucity of preference data per reviewer or per paper (relative to other recommender systems applications) we show how we can integrate multiple sources of information to learn reviewer-paper preference models. Our models are evaluated not just in terms of prediction accuracy but in terms of end-assignment quality. Using a linear programming-based assignment optimization, we show how our approach better explores the space of unsupplied assignments to maximize the overall affinities of papers assigned to reviewers. We demonstrate our results on real reviewer bidding data from the IEEE ICDM 2007 conference.

Bipartite Graph Matching Computation on GPU

Abstract: The Bipartite Graph Matching Problem is a well studied topic in Graph Theory. Such matching relates pairs of nodes from two distinct sets by selecting a subset of the graph edges connecting them. Each edge selected has no common node as its end points to any other edge within the subset. When the considered graph has huge sets of nodes and edges the sequential approaches are impractical, specially for applications demanding fast results. In this paper we investigate how to compute such matching on Graphics Processing Units (GPUs) motivated by its increasing processing power made available with decreasing costs. We present a new data-parallel approach for computing bipartite graph matching that is efficiently computed on today's graphics hardware and apply it to solve the correspondence between 3D samples taken over a time interval.

Discrete invasive weed optimization algorithm: application to cooperative multiple task assignment of UAVs

Abstract: This paper presents a novel discrete population based stochastic optimization algorithm inspired from weed colonization. Its performance in a discrete benchmark, time-cost trade-off (TCT) problem, is evaluated and compared with five other evolutionary algorithms. Also we use our proposed discrete invasive weed optimization (DIWO) algorithm for cooperative multiple task assignment of unmanned aerial vehicles (UAVs) and compare the solutions with those of genetic algorithms (GAs) which have shown satisfactory results in the previous works. UAV task assignment problem is of great interest among researchers and many deterministic and stochastic methods have been devised to come up with the problem. Monte Carlo simulations show successful results that verify better performance of DIWO compared to GAs in both optimality of the solutions and computational time.