Topic
Assignment problem
About: Assignment problem is a research topic. Over the lifetime, 7588 publications have been published within this topic receiving 172820 citations. The topic is also known as: marriage problem.
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19 Jun 2003
TL;DR: This paper compares two algorithms for Multiple Target Tracking, using Global Nearest neighbor (GNN) and Suboptimal Nearest Neighbor (SNN) approach respectively and results reveal that in some cases the GNN approach gives batter solution than the SNN approach.
Abstract: This paper compares two algorithms for Multiple Target Tracking (MTT), using Global Nearest Neighbor (GNN) and Suboptimal Nearest Neighbor (SNN) approach respectively. For both algorithms the observations are divided in clusters to reduce computational efforts. For each cluster the assignment problem is solved by using Munkres algorithm or according SNN rules. Results reveal that in some cases the GNN approach gives batter solution than.SNN approach. The computational time, needed for assignment problem solution using Munkres algorithm is studied and results prove that it is suitable for real time implementations.
209 citations
09 Dec 2009
TL;DR: The 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, and an algorithm is provided that achieves a competitive ratio of 1 ?
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.
209 citations
Book•
30 Sep 1987TL;DR: The Motivations for Distributed Processing of Serial Programs is a guide to finding the Optimal Assignment across Space and Time and Formulation of the Problem.
Abstract: 1. Introduction.- 1.1. The Motivations for Distributed Processing.- 1.1.1. Distributed Processing of Serial Programs.- 1.1.2. Parallel Processing.- 1.2. Environments for Distributed Processing.- 1.3. Distinction between Distributed and Parallel Processing.- 1.4. The Central Problem Addressed in this book.- 1.5. Graph-Theoretic Solution Techniques.- 1.6. Overview.- 2. Graph Theoretic Concepts.- 2.1. Directed Graphs.- 2.1.1. Basic Definitions.- 2.1.2. Paths in Directed Graphs.- 2.2. Undirected Graphs.- 2.2.1. Basic Definitions.- 2.2.2. Paths in Undirected Graphs.- 2.3. Graphs in General.- 2.3.1. Subgraphs.- 2.3.2. The Underlying Graph of a Directed Graph.- 2.3.3. Connected Components of a Graph.- 2.3.4. Cutsets.- 2.3.5. s-t cuts.- 2.4. Weighted Graphs.- 2.4.1. Shortest Paths.- 2.4.2. Mincuts.- 2.5. Trees.- 2.5.1. Directed Trees.- 2.5.2. Binary Trees.- 2.6. Multigraphs.- 2.7. Further Reading.- 3. Network Flow Techniques.- 3.1. The Basic Dual-Processor Assignment Problem.- 3.1.1. Stone's Solution to the Assignment Problem.- 3.1.2. Applications.- 3.2. Memory Constraints.- 3.3. Dynamic Assignments.- 3.3.1. Solution to the Dynamic Assignment Problem.- 3.3.2. Zero Residence Cost Graphs.- 3.3.3. Relationship between Dynamic and Static Graphs.- 3.3.4. Bounds on the costs of the Dynamic Assignment.- 3.3.5. An Alternative Problem Formulation.- 3.4. Resource Partitioning with Replication.- 3.5. Summary.- 4. The Shortest Tree Algorithm.- 4.1. Introduction.- 4.2. Assigning Trees across Space.- 4.2.1. Formulation of the Problem.- 4.2.2. The Assignment Graph.- 4.2.3. The Shortest Tree Algorithm.- 4.3. Assigning Series-Parallel Graphs.- 4.3.1. Definitions.- 4.3.2. The Assignment Graph.- 4.3.3. Finding the Optimal Assignment.- 4.4. Optimal Assignments across Space and Time.- 4.4.1. Motivations.- 4.4.2. Formulation of the Problem.- 4.4.3. Solution.- 4.5. Summary.- 5. Varying Load Conditions.- 5.1. Varying Load on one Processor.- 5.1.1. Formulation.- 5.1.2. Critical Load Factors.- 5.1.3. Applications.- 5.2. Varying Load on Two Processors.- 5.2.1. Formulation.- 5.2.2. The Load Plane.- 5.2.3. Finding the Load Plane.- 5.2.4. Critical Load Lines.- 5.3. Varying Communication Costs.- 5.4. Summary.- 6. Sum-Bottleneck Algorithm.- 6.1. Motivations.- 6.2. Definitions.- 6.3. Partitioning Chains over Chains.- 6.3.1. Signal Processing.- 6.3.2. Image Analysis.- 6.3.3. Partial Differential Equations.- 6.3.4. Execution and Communication Costs.- 6.3.5. Construction of Assignment Graph.- 6.3.6. Finding the Optimal Assignment.- 6.4. Partitioning Multiple Chains in a Host-Satellite System.- 6.4.1. Construction of the Assignment Graph.- 6.4.2. Solution.- 6.5. Global Assignments in Multiple-Satellite System.- 6.5.1. Transformation into Chains.- 6.5.2. Construction of the Assignment Graph.- 6.6. Partitioning Trees in a Host-Satellite System.- 6.6.1. Construction of the Assignment Graph.- 6.7. Summary.- 7. Mapping for Parallel Processing.- 7.1. The Parallel Processing Environment.- 7.2. The Mapping Problem.- 7.2.1. Definitions.- 7.2.2. Applications.- 7.2.3. Relation to Graph Isomorphism.- 7.2.4. A Heuristic algorithm.- 7.3. Binary Dissections of Non-uniform domains.- 7.3.1. The Binary Dissection Strategy.- 7.3.2. Natural mappings.- 7.4. Related Research.- 7.4.1. Extensions of the Mapping Problem.- 7.4.2. Other Interconnection Structures.- 7.5. Summary.- 8. Conclusions.- 8.1. Alternative Approaches.- 8.2. Open Problems.- 8.3. Sources of Information.
208 citations
TL;DR: A fast algorithm for oflline computing of an optimal schedule is given, and it is shown that finding an optimal offline schedule is at least as hard as the assignment problem.
Abstract: In the k-server problem, one must choose how k mobile servers will serve each of a sequence of requests, making decisions in an online manner. An optimal deterministic online strategy is exhibited when the requests fall on the real line. For the weighted-cache problem, in which the cost of moving to x from any other point is $w( x )$, the weight of x, an optimal deterministic algorithm is also provided. The nonexistence of competitive algorithms for the asymmetric two-server problem and of memoryless algorithms for the weighted-cache problem is proved. A fast algorithm for oflline computing of an optimal schedule is given, and it is shown that finding an optimal offline schedule is at least as hard as the assignment problem.
208 citations
TL;DR: This survey paper reviews results on heuristics for two weighted matching problems: matchings where the vertices are points in the plane and weights are Euclidean distances, and the assignment problem.
Abstract: This survey paper reviews results on heuristics for two weighted matching problems: matchings where the vertices are points in the plane and weights are Euclidean distances, and the assignment problem. Several heuristics are described in detail and results are given for worst-case ratio bounds, absolute bounds, and expected bounds. Applications to practical problems and some mathematical complements are also included.
206 citations