
Combinatorial Optimization and Applications
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Content
- Intro
- Preface
- Organization
- Contents
- Classic Combinatorial Optimization
- Improved Algorithms for the Evacuation Route Planning Problem
- 1 Introduction
- 2 Related Work
- 3 Problem Definition and Model
- 4 The Single Source Single Sink Problem
- 4.1 Limitation of QPER Algorithm for SSEP
- 4.2 Modified Algorithm for SSEP When We Are Given k Edge-Disjoint Paths
- 4.3 An Important Observation
- 4.4 Our Algorithm for SSEP
- 4.5 Running Time Analysis of SSEP
- 4.6 CCRP Algorithm for SSEP and Some Observations
- 4.7 Analysis of Algorithm [1]
- 5 Randomized Behavior Model of People
- 5.1 Lower Bound for Expected Evacuation Time
- 5.2 Algorithm for Randomized Behavior of People
- 6 Experimental Results
- 6.1 Details of the Experiments
- 6.2 Results
- 7 Conclusion and Future Work
- References
- Improved MaxSAT Algorithms for Instances of Degree 3
- 1 Introduction
- 2 Reduction Rules
- 3 An O*(1.194k)-time Parameterized Algorithm
- 4 An O*(1.237n)-time Algorithm for (n,3)-MaxSAT
- 5 Conclusion
- References
- Directed Pathwidth and Palletizers
- 1 Introduction
- 2 Preliminaries
- 3 Main Result
- 4 Applications
- 4.1 Hardness Result
- 4.2 Bounded FIFO Stack-Up Systems
- 4.3 Approximation
- 5 Conclusion
- References
- Black and White Bin Packing Revisited
- 1 Introduction
- 2 Algorithm ``Balance Between Stacks''
- 2.1 Description of Algorithm BAL
- 3 Competitive Analysis of Algorithm BAL
- 3.1 Terminology and Case Analysis
- 3.2 A Function Calculating the Total Size of Bins
- 3.3 Case by Case Analysis of the Competitive Ratio of BAL
- 4 Concluding Remarks
- References
- Local Search Algorithms for k-Median and k-Facility Location Problems with Linear Penalties
- 1 Introduction
- 2 General Local Search Algorithm
- 3 Local Search for k-MPLP
- 3.1 Analysis
- 4 Local Search for k-FLPLP
- 4.1 Analysis
- 4.2 Improve the Local Gap Using Scaling Technique
- 5 Polynomial-Time Algorithm for k-MPLP and k-FLPLP
- References
- A (5.83+)-Approximation Algorithm for Universal Facility Location Problem with Linear Penalties
- 1 Introduction
- 2 Local Search Algorithm
- 2.1 Operations
- 2.2 Polynomial-Time Proof
- 2.3 Algorithm
- 3 Analysis
- 4 Discussions
- References
- Variants of Multi-resource Scheduling Problems with Equal Processing Times
- 1 Introduction
- 2 Literature Review, Framework and Notations
- 2.1 Related Work
- 2.2 Objective Functions
- 2.3 Network Flows
- 2.4 Scheduling Graph
- 3 Variety of Machines
- 4 General Objective Function
- 5 Monotonic Objective Function
- 6 Periodic Objective Function
- 6.1 Scheduling Problem as a Network Flow
- 6.2 Periodic Objective Function Formulated as a Network Flow
- 7 Additional Remark
- 8 Conclusion
- References
- Geometric Optimization
- The Discrete and Mixed Minimax 2-Center Problem
- 1 Introduction
- 2 The Discrete Minimax 2-Center Problem
- 3 The Mixed Minimax 2-Center Problem
- 3.1 The Structure of the Optimal Solution
- 3.2 Solving MMM2CP for a Fixed p and r
- 3.3 The Monotone Property
- 4 Conclusion
- References
- Approximation Algorithms for Generalized MST and TSP in Grid Clusters
- 1 Introduction
- 2 The GGMST Approximation Algorithm
- 3 The Lower Bound Proof
- 4 Approximation of the GGTSP
- 5 Conclusions
- References
- Covering, Hitting, Piercing and Packing Rectangles Intersecting an Inclined Line
- 1 Introduction
- 2 Set Cover and Hitting Set Problems
- 2.1 Unit Squares Intersecting a Diagonal Line
- 2.2 Unit-Height Rectangles Intersecting a Diagonal Line
- 2.3 Unit Squares Touching a Diagonal Line
- 3 Piercing Set Problem
- 3.1 Rectangles Intersecting a Diagonal Line
- 3.2 Unit Squares Intersecting a Diagonal Line
- 4 Independent Set Problem
- 4.1 Squares Intersecting a Diagonal Line
- 4.2 Unit-Height Rectangles Intersecting a Diagonal Line
- References
- Optimal Self-assembly of Finite Shapes at Temperature 1 in 3D
- 1 Introduction
- 2 Definitions
- 2.1 3D Abstract Tile Assembly Model
- 2.2 Complexities of (Scaled) Finite Shapes
- 3 Main Theorem
- 4 Main Construction
- 4.1 Setup
- 4.2 Seed Block
- 4.3 Growth Blocks
- 4.4 Putting It All Together
- 5 Conclusion
- References
- Line Segment Covering of Cells in Arrangements
- 1 Introduction
- 2 NP-hardness for Rectilinear Line Segments
- 2.1 Reduction
- 2.2 Correctness
- 3 Covering Only Rectangular Cells
- 3.1 NP-hardness
- 3.2 FPT on the Size of the Optimal Solution
- 4 Rectangular Subdivisions
- 5 Conclusions and Open Problems
- References
- An Improved On-line Strategy for Exploring Unknown Polygons
- 1 Introduction
- 2 Preliminaries
- 2.1 An Overview of the 2-approximation Algorithm
- 2.2 An Overview of the 26.5-Competitive Strategy
- 3 Exploring a Right Polygon
- 3.1 How to Reach the Cut of a Right Vertex at the Wanted Point
- 3.2 The Exploration Strategy
- 3.3 The Performance Analysis
- 4 Exploring a Simple Polygon
- 4.1 The 6.7-Competitive Strategy
- References
- Polynomial Time Approximation Scheme for Single-Depot Euclidean Capacitated Vehicle Routing Problem
- 1 Introduction
- 2 Problem Statement
- 3 Iterated Tour Partition Heuristic
- 4 Approximation of TSP in R3
- 5 Polynomial Time Approximation Scheme for Capacitated Vehicle Routing Problem in 3-Dimensional Space
- 6 Conclusion
- References
- Network Optimization
- A Fast and Effective Heuristic for Discovering Small Target Sets in Social Networks
- 1 Introduction
- 2 The Model, the Context, and Our Results
- 2.1 Related Work
- 2.2 Our Results
- 3 The TSS Algorithm
- 4 Estimating the Size of the Solution
- 5 Proofs of Optimality
- 6 Computational Experiments
- 6.1 Random Graphs
- 6.2 Large Real-Life Networks
- 7 Concluding Remarks
- References
- An Efficient Shortest-Path Routing Algorithm in the Data Centre Network DPillar
- 1 Introduction
- 2 The DCN DPillar
- 3 Abstracting Routing in DPillar
- 3.1 Another Abstraction: The Marked Cycle
- 4 Routing in a Marked Cycle
- 4.1 A Shortest Path has at Most Two Turns
- 5 An Optimal Routing Algorithm for DPillar
- 5.1 Building Our Set of Paths When x =0
- 5.2 Building Our Set of Paths When x = 0
- 5.3 Our Algorithm
- 6 Conclusions
- References
- A Sensor Deployment Strategy in Bus-Based Hybrid Ad-Hoc Networks
- 1 Introduction
- 2 Related Work
- 3 Network Model
- 4 Problem Definition and Assumptions
- 5 Sensor Deployment Scheme
- 5.1 Simple Large Regions Without Boundaries
- 5.2 Large Regions with Boundaries
- 6 Simulations
- 6.1 Simulation Scenarios
- 6.2 Simulation Analysis for Sensor Deployment
- 6.3 Simulation Analysis for Average Delay
- 7 Conclusion and Future Works
- References
- New Insight into 2-Community Structures in Graphs with Applications in Social Networks
- 1 Introduction
- 2 Preliminaries
- 3 2-Community Structure in 3-Regular Graphs
- 4 Balanced 2-Community Structure
- 5 Conclusion and Open Problems
- References
- WDCS: A Weight-Based Distributed Coordinate System
- 1 Introduction
- 2 Problem Formulation
- 3 WDCS: A High-Precision Scheme
- 3.1 Overview Of WDCS
- 3.2 Details of WDCS
- 4 Experimental Results
- 4.1 Evaluation Metrics
- 4.2 Accuracy
- 4.3 Convergence Behaviour
- 5 Conclusion
- References
- Adaptive Scheduling Over a Wireless Channel Under Constrained Jamming
- 1 Introduction
- 2 Model
- 3 Uniform Packets
- 4 Optimal Algorithm for f= 1
- 5 Optimal Algorithm for ANY f& 1
- 6 Discussion
- References
- Metric and Distributed On-Line Algorithm for Minimizing Routing Interference in Wireless Sensor Networks
- 1 Introduction
- 2 Related Works
- 3 Interference Metric
- 3.1 Network Model
- 3.2 Quantifying Interference Level
- 3.3 Analysis of Interference Metric
- 4 Distributed On-Line Algorithm
- 4.1 Description of DOAMI
- 5 Simulation Results
- 6 Conclusion
- References
- Distributed Algorithm for Mending Barrier Gaps via Sensor Rotation in Wireless Sensor Networks
- 1 Introduction and Related Works
- 2 Network Model and Problem Definition
- 3 Distributed Algorithm for Weak Barrier Coverage
- 3.1 Phase 1: Neighbor Discovery
- 3.2 Phase 2: Optimal Orientation
- 3.3 Phase 3: Minimizing the Gap Length
- 4 Simulation Results
- 5 Conclusions
- References
- Applied Optimization
- A Hybrid Large Neighborhood Search for Dynamic Vehicle Routing Problem with Time Deadline
- 1 Introduction
- 2 Problem Formulation
- 3 Hybrid Large Neighborhood Search
- 3.1 Insert Heuristic
- 3.2 Large Neighborhood Search
- 4 Computational Results
- 4.1 Static Results and Analysis
- 4.2 Dynamic Results and Analysis
- 5 Conclusion
- References
- Indoor Localization via Candidate Fingerprints and Genetic Algorithm
- 1 Introduction
- 2 Related Work
- 3 Problem Formulation
- 4 Pick the CFs
- 5 Search Closest Fingerprint Using GA
- 5.1 Example Scenario
- 5.2 The Genetic Algorithm
- 6 Performance Evaluation
- 6.1 Analytical Model for Selecting CFs
- 6.2 The Effect of CFs Selecting
- 6.3 The Effect of Communication Distance
- 6.4 Localization Errors
- 7 Conclusion
- References
- On Clustering Without Replication in Combinatorial Circuits
- 1 Introduction
- 2 Graph Preliminaries
- 3 Statement of Problems
- 4 Related Work
- 5 Computational Complexity of CN
- 6 A 2-Approximation Algorithm for CN"426830A N, 2, "526930B
- 7 Conclusion
- References
- On Replica Placement in High-Availability Storage Under Correlated Failure
- 1 Introduction
- 2 Model
- 3 An O(n2) Greedy Algorithm
- 4 Balanced Placements
- 5 An O(n + log) Algorithm
- 5.1 Divide Phase
- 5.2 Combine Phase
- 5.3 Transform Phase
- 6 Conclusion and Future Work
- References
- Observing the State of a Smart Grid Using Bilevel Programming
- 1 Introduction
- 2 Problem Statement
- 2.1 Observability of a Graph
- 3 Mathematical Modelling
- 3.1 Iterative Model
- 3.2 From Iterative to Bilevel Model
- 3.3 Bilevel Model
- 4 An Algorithm for the Bilevel Problem
- 5 Computational Results
- 6 Conclusions
- References
- Optimizing Static and Adaptive Probing Schedules for Rapid Event Detection
- 1 Introduction
- 1.1 Our Contribution
- 2 Related Work
- 3 Model and Problem Definition
- 4 Results
- 4.1 On Maximizing Immediate Gain
- 4.2 Lower Bound on Optimal Cost
- 4.3 Deterministic (3+(c-1)/c)-Approximation Schedule
- 4.4 On Optimal Memoryless Schedule
- 4.5 On Adaptive Algorithm for Memoryless Schedules
- References
- Complexity and Game
- Vertex Cover in Conflict Graphs: Complexity and a Near Optimal Approximation
- 1 Introduction
- 1.1 Database Application
- 1.2 Literature Review of the Vertex Cover Problem
- 1.3 Our Contribution
- 2 Complexity and Inapproximation
- 3 A Near Optimal ( 2-12r)-approximation
- 3.1 A Basic Approximation Algorithm
- 3.2 Improve the Approximation by Triangle Eliminating
- 3.3 Near Optimality
- References
- On the Complexity of Scaffolding Problems: From Cliques to Sparse Graphs
- 1 Introduction
- 2 Notation and Problem Description
- 3 Dense Graphs
- 3.1 Good News
- 3.2 Bad News
- 4 Sparse Graphs
- 4.1 Bad News
- 4.2 Good News
- 5 Conclusion
- References
- Parameterized Lower Bound and NP-Completeness of Some H-Free Edge Deletion Problems
- 1 Introduction
- 2 Preliminaries and Basic Tools
- 2.1 Basic Tools
- 3 T-free Edge Deletion
- 3.1 Base Cases
- 3.2 Induction
- 4 R-free Edge Deletion
- 5 Handling Disconnected Graphs
- 6 Concluding Remarks
- References
- Multicast Network Design Game on a Ring
- 1 Introduction
- 2 Preliminaries
- 3 Price of Anarchy/Stability for Multicast on Rings
- 4 Potential-Optimum Price of Anarchy for Multicast on Rings
- 5 Myopic Sequential Prices of Anarchy/Stability
- 5.1 Sequential Price of Anarchy in Multicast Game on Rings
- 5.2 Myopic Sequential Price of Stability in Multicast Game
- 5.3 Myopic Sequential Price of Stability on Rings
- 6 Conclusions
- A Weights for Inequalities from the Proof of Theorem??
- References
- Extreme Witnesses and Their Applications
- 1 Introduction
- 2 Preliminaries
- 3 Extreme Witnesses for Boolean Convolution
- 3.1 String Matching
- 3.2 (min, +) Convolution
- 4 Extreme Witnesses for Boolean Matrix Product
- 4.1 Lightest Triangles
- 5 Final Remarks
- References
- Orbital Independence in Symmetric Mathematical Programs
- 1 Introduction
- 2 Previous Work and Notation
- 2.1 Mathematical Programming
- 2.2 Symmetry Detection
- 2.3 Formulation and Solution Groups
- 2.4 Symmetry Breaking Constraints
- 2.5 Orbits
- 2.6 Strong and Weak SBCs
- 2.7 Stabilizers
- 3 Orbital Independence Notions
- 3.1 Incompatible SBCs
- 3.2 Some Existing OI Conditions
- 3.3 New Conditions for OI
- 3.4 SBCs from Independent Sets
- 4 Orbital Independence Algorithm
- 4.1 Independence Graph
- 4.2 Orbital Independence Reformulations
- 4.3 Algorithm Description
- 5 Computational Experiments
- 5.1 Environment
- 5.2 Results
- 6 Conclusions
- References
- Symbolic Model Checking for Alternating Projection Temporal Logic
- 1 Introduction
- 2 Alternating Projection Temporal Logic
- 2.1 APTL Syntax
- 2.2 APTL Semantics
- 2.3 Normal Form of APTL
- 3 Interpreted Systems and Symbolization
- 3.1 Interpreted Systems
- 3.2 Symbolic Representation of System Models
- 4 Symbolic Model Checking for APTL
- 4.1 Symbolic Model Checking Algorithm for APTL
- 4.2 Model Checker MCMAS_APTL
- 4.3 A Case Study
- 5 Conclusions
- References
- Optimization in Graphs
- An I/O Efficient Algorithm for Minimum Spanning Trees
- 1 Introduction
- 2 The Stages
- 3 A Phase
- 4 A Proof of Correctness
- 5 The I/O Complexity
- References
- The Connected p-Centdian Problem on Block Graphs
- 1 Introduction
- 2 Problem Formulation
- 3 The CpM Problem on Block Graph with Unit Edge Length
- 4 The Connected p-Centdian Problem on Unweighted Block Graphs
- 5 An Example for the Connected p-Centdian Problem
- References
- Searching for (near) Optimal Codes
- 1 Introduction
- 2 Preliminaries
- 3 New Binary Linear Codes Searching from Circulant Graphs
- 4 New Additive Codes Searching from Circulant Graphs
- 5 Concluding Remarks
- References
- Dynamic Single-Source Shortest Paths in Erdös-Rényi Random Graphs
- 1 Introduction
- 1.1 Previous Work
- 1.2 Our Results
- 2 Ding and Lin's Local Search Algorithm
- 2.1 Preliminaries
- 2.2 Local Search Algorithm
- 3 Weight Increase in Weighted ER Random Graphs
- 3.1 ER and Weighted ER Random Graphs
- 3.2 Fundamental Lemmas
- 3.3 Expected Update Time in Weighted ER Random Graphs
- 4 Edge Deletion in ER Random Graphs
- 5 Concluding Remarks
- References
- Trees, Paths, Stars, Caterpillars and Spiders
- 1 Introduction
- 2 Linear Arboricity of Bipartite Graphs
- 2.1 K2k-1,2k and Tc
- 2.2 Linear Arboricity 2
- 2.3 Linear Arboricity k for k 3
- 3 Star Arboricity of Bipartite Graphs
- 4 Caterpillar Arboricity of Bipartite Graphs
- 5 Spider Arboricity of Bipartite Graphs
- 6 Concluding Remarks
- References
- Algorithms for the Densest Subgraph with at Least k Vertices and with a Specified Subset
- 1 Introduction
- 2 Definitions
- 3 An Algorithm for DalkS Based on the Minimum s-t Cut with at Least k Vertices
- 4 A Greedy Approximation Algorithm for DSS
- 5 Conclusion
- References
- Deleting Edges to Restrict the Size of an Epidemic: A New Application for Treewidth
- 1 Introduction
- 1.1 Review of Previous Work
- 1.2 Notation and Problem Definition
- 1.3 Tree Decompositions
- 2 Treewidth of Real Networks
- 3 The Algorithm
- 3.1 The Signature of a Node
- 3.2 Running Time and Extensions
- 4 Conclusions and Open Problems
- References
- Optimal Approximation Algorithms for Maximum Distance-Bounded Subgraph Problems
- 1 Introduction
- 2 Problems and Previous Results
- 2.1 Definitions
- 2.2 Optimal Approximation Algorithm for Max d-Club with Even d in [3]
- 3 Optimal Approximation Algorithm for Max d-Club with Odd d
- 4 Polynomial-Time Algorithms of Max d-Club for Graph Classes
- 4.1 Graph Classes
- 4.2 Algorithms
- 4.3 Chordal and Weakly Chordal Graphs for Odd d
- 4.4 Strongly Chordal, Trapezoid, and Interval Graphs
- 5 Max d-Clique
- References
- The Influence of Preprocessing on Steiner Tree Approximations
- 1 Introduction
- 2 Approximation Algorithms and Their Engineering
- 3 Preprocessing Techniques
- 4 Experimental Evaluation
- 5 Conclusion
- A Distribution of Solution Values
- B More Detailed Table for Influence of Preprocessing
- References
- Legally (+2)-Coloring Bipartite Outerplanar Graphs in Cubic Time
- 1 Introduction
- 2 Bipartite Outerplanar Graphs with =3
- 3 Bipartite Outerplanar Graphs with 4
- 3.1 Ordered Breadth First Search
- 3.2 A Legal (+2)-coloring Algorithm
- References
- Maximum Independent Set on B1-VPG Graphs
- 1 Introduction
- 2 Preliminaries
- 3 Approximation for B1-VPG
- 4 Analysis of IndSet1 and IndSet2
- 4.1 Analysis of Running Time
- 5 Approximation for Equilateral B1-VPG:
- 6 Hardness of MIS on Unit L-Graphs
- 7 Conclusion and Remarks
- References
- Approximating the Restricted 1-Center in Graphs
- 1 Introduction
- 2 Problem Definitions and Intractability
- 3 An FPTAS for RV1CP
- 4 Approximation Algorithms for RA1CP
- 4.1 Fundamental Properties
- 4.2 Approximation Algorithms
- 5 Concluding Remarks
- References
- The Disjunctive Bondage Number and the Disjunctive Total Bondage Number of Graphs
- 1 Introduction
- 2 Preliminaries
- 3 The Disjunctive Bondage Number of Graphs
- 3.1 Some Exact Values
- 3.2 Some Upper Bounds
- 4 The Disjunctive Total Bondage Number of Some Graphs
- 5 Closing Remark
- References
- Edge-Disjoint Packing of Stars and Cycles
- 1 Introduction
- 2 Hardness Results
- 3 Kernelization Results
- 3.1 Kernelization for Edge-Disjoint k-Packing of s-Stars
- 3.2 Kernelization for Edge-Disjoint k-Packing of 4-Cycles
- References
- Dynamic Minimum Bichromatic Separating Circle
- 1 Introduction
- 1.1 Related Work
- 1.2 Our Results
- 2 A Unified Approach for Insertion/Deletion of Blue Points
- 3 Logarithmic Query for Insertions
- 4 Conclusions and Future Work
- References
- Miscellaneous
- Searching Graph Communities by Modularity Maximization via Convex Optimization
- 1 Introduction
- 2 Preliminaries
- 3 Problem Definition
- 3.1 The Convex Optimization Problem
- 3.2 CAR - Convex Optimization Based Accurate Rounding Algorithm
- 4 Conclusion
- References
- A New Tractable Case of the QAP with a Robinson Matrix
- 1 Introduction
- 2 Conic Representation of Specially Structured Matrices
- 2.1 Cut Weights and Specially Structured Matrices
- 2.2 Recognizing Conic Combinations of Cut Matrices in CDW Normal Form
- 3 Conclusions
- References
- An Online Model of Berth and Quay Crane Integrated Allocation in Container Terminals
- 1 Introduction
- 1.1 Related Work
- 2 Problem Description and Basic Notations
- 3 The Online Algorithm and Its Basic Properties
- 3.1 Algorithm Description
- 3.2 Basic Properties
- 4 Competitive Analysis of Algorithm GLR
- 5 A Matching Lower Bound
- 6 Conclusion
- References
- On the Minimal Constraint Satisfaction Problem: Complexity and Generation
- 1 Introduction
- 2 The Minimal CSP: Definitions and Complexity
- 2.1 Definitions
- 2.2 Complexity
- 3 Generating Minimal CSP Instances
- 3.1 Preliminary Notions
- 3.2 The Generator
- 3.3 Behavior of the Minimal CSP
- 4 Conclusion
- References
- Algebraic Theory on Shortest Paths for All Flows
- 1 Introduction
- 2 Single Source Shortest Path Problem
- 3 Single Source Bottleneck Path Problem
- 4 Single Source Shortest Paths for All Flows
- 5 A Faster Algorithm for SSSP-AF
- 6 Single Source Bottleneck Paths for All Costs Problem (SSBP-AC)
- 7 Concluding Remarks
- References
- The Minimum Acceptable Violation Ranking of Alternatives from Voters' Ordinal Rankings
- 1 Introduction
- 2 Formulation
- 2.1 Preliminaries
- 2.2 Minimum Acceptable Violation Ranking Model
- 3 Ranking Procedure
- 3.1 Branch-and-Bound Ranking Procedure
- 3.2 A Numerical Example
- 4 Numerical Experiments
- 5 Conclusions
- References
- Listing Center Strings Under the Edit Distance Metric
- 1 Introduction
- 2 Related Work
- 3 Preliminaries
- 3.1 Edit Distance
- 4 Listing Center Strings
- 4.1 Algorithm ListBall: Listing Strings within Distance d
- 4.2 Listing Center Strings
- 5 Listing Common Subsequences
- 6 Concluding Remarks
- References
- Online Scheduling for Electricity Cost in Smart Grid
- 1 Introduction
- 2 Preliminaries
- 3 Algorithm and Competitive Analysis
- 4 Conclusions and Remarks
- References
- Proportional Cost Buyback Problem with Weight Bounds
- 1 Introduction
- 2 Preliminaries
- 3 The Matroid Constraint
- 3.1 An Optimal Online Algorithm
- 3.2 Lower Bound
- 4 The Unweighted Knapsack Constraint
- 4.1 Optimal Online Algorithms
- 4.2 Lower Bound for the Knapsack Constraint Case
- References
- Author Index
- Erratum to: On Replica Placement in High-Availability Storage Under Correlated Failure
- Erratum to: Chapter 26: Z. Lu et al. (Eds.) Combinatorial Optimization and Applications DOI: 10.1007/978-3-319-26626-8_26
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