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The bandwidth problem for graphs and matrices—a survey
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
inferredcites →https://doi.org/10.1002/nme.1620020406openalex-snapshot
An automatic reordering scheme for simultaneous equations derived from network systems
inferredcites →https://doi.org/10.1002/nme.1620060306openalex-snapshot
Bandwidth reduction by automatic renumbering
inferredcites →https://doi.org/10.1002/nme.1620100406openalex-snapshot
An automatic node relabelling scheme for minimizing a matrix or network bandwidth
inferredcites →https://doi.org/10.1002/nme.1620140606openalex-snapshot
A comparasion of three resequencing algorithms for the reduction of matrix profile and wavefront
inferredcites →https://doi.org/10.1007/978-1-4615-8675-3_14openalex-snapshot
Several Strategies for Reducing the Bandwidth of Matrices
inferredcites →https://doi.org/10.1007/bf02239468openalex-snapshot
Note on minimizing the bandwidth of sparse, symmetric matrices
inferredcites →https://doi.org/10.1007/bf02252900openalex-snapshot
Minimizing the bandwidth of sparse symmetric matrices
inferredcites →https://doi.org/10.1007/bf02280884openalex-snapshot
The NP-Completeness of the bandwidth minimization problem
inferredcites →https://doi.org/10.1007/bf02521587openalex-snapshot
Reducing the profile of sparse symmetric matrices
inferredcites →https://doi.org/10.1016/0012-365x(75)90039-4openalex-snapshot
Optimal labelling of a product of two paths
inferredcites →https://doi.org/10.1016/0012-365x(76)90051-0openalex-snapshot
The factorial representation of balanced labelled graphs
inferredcites →https://doi.org/10.1016/0304-3975(76)90059-1openalex-snapshot
Some simplified NP-complete graph problems
inferredcites →https://doi.org/10.1016/b978-1-4832-3187-7.50008-8openalex-snapshot
HOW TO NUMBER A GRAPH††This research was supported in part by the United States Air Force under Grant AFOSR-68-1555.
inferredcites →https://doi.org/10.1016/b978-1-4832-3187-7.50018-0openalex-snapshot
A GRAPH-THEORETIC STUDY OF THE NUMERICAL SOLUTION OF SPARSE POSITIVE DEFINITE SYSTEMS OF LINEAR EQUATIONS
inferredcites →https://doi.org/10.1016/s0021-9800(66)80059-5openalex-snapshot
Optimal numberings and isoperimetric problems on graphs
inferredcites →https://doi.org/10.1016/s0167-5060(08)70323-6openalex-snapshot
Sequencing Jobs to Minimize Total Weighted Completion Time Subject to Precedence Constraints
inferredcites →https://doi.org/10.1061/jmcea3.0001349openalex-snapshot
Bandwidth Minimization of Stiffness Matrices
inferredcites →https://doi.org/10.1061/jsdeag.0003109openalex-snapshot
Algorithm for Matrix Bandwidth Reduction
inferredcites →https://doi.org/10.1061/jsdeag.0003409openalex-snapshot
Discussion of “Algorithm for Matrix Bandwidth Reduction”
inferredcites →https://doi.org/10.1061/jsdeag.0003997openalex-snapshot
Node Numbering Optimization in Structural Analysis
inferredcites →https://doi.org/10.1061/jyceaj.0002316openalex-snapshot
Efficient Code for Steady-State Flows in Networks
inferredcites →https://doi.org/10.1080/03601217608907288openalex-snapshot
Reducing the Bandwidth of Structural Stiffness Matrices
inferredcites →https://doi.org/10.1090/s0025-5718-1974-0379289-6openalex-snapshot
Optimal Indexing of the Vertices of Graphs
inferredcites →https://doi.org/10.1093/comjnl/10.3.300openalex-snapshot
Row-column permutation of sparse matrices
inferredcites →https://doi.org/10.1093/comjnl/3.1.34openalex-snapshot
The Analysis of Large Structural Systems
inferredcites →https://doi.org/10.1093/comjnl/8.3.264openalex-snapshot
An algorithm for reducing the bandwidth of a matrix of symmetrical configuration
inferredcites →https://doi.org/10.1109/proc.1977.10517openalex-snapshot
Applications of numbered undirected graphs
inferredcites →https://doi.org/10.1111/j.1749-6632.1970.tb56468.xopenalex-snapshot
ON PRIMITIVE GRAPHS AND OPTIMAL VERTEX ASSIGNMENTS
inferredcites →https://doi.org/10.1137/0112012openalex-snapshot
Optimal Assignments of Numbers to Vertices
inferredcites →https://doi.org/10.1137/0134037openalex-snapshot
Complexity Results for Bandwidth Minimization
inferredcites →https://doi.org/10.1137/0601042openalex-snapshot
Dynamic-Programming Algorithms for Recognizing Small-Bandwidth Graphs in Polynomial Time
inferredcites →https://doi.org/10.1137/0713020openalex-snapshot
Comparative Analysis of the Cuthill–McKee and the Reverse Cuthill–McKee Ordering Algorithms for Sparse Matrices
inferredcites →https://doi.org/10.1137/0713023openalex-snapshot
An Algorithm for Reducing the Bandwidth and Profile of a Sparse Matrix
inferredcites →https://doi.org/10.1137/0715021openalex-snapshot
Algorithms for Matrix Partitioning and the Numerical Solution of Finite Element Systems
inferredcites →https://doi.org/10.1145/1499799.1499935openalex-snapshot
Another algorithm for reducing bandwidth and profile of a sparse matrix
inferredcites →https://doi.org/10.1145/355705.355707openalex-snapshot
A Comparison of Several Bandwidth and Profile Reduction Algorithms
inferredcites →https://doi.org/10.1145/355705.355712openalex-snapshot
Algorithm 508: Matrix Bandwidth and Profile Reduction [F1]
inferredcites →https://doi.org/10.1145/355705.355713openalex-snapshot
Algorithm 509: A Hybrid Profile Reduction Algorithm [F1]
inferredcites →https://doi.org/10.1145/360767.360783openalex-snapshot
Tridiagonalization by permutations
inferredcites →https://doi.org/10.1145/800119.803884openalex-snapshot
Some simplified NP-complete problems
inferredcites →https://doi.org/10.1145/800195.805928openalex-snapshot
Reducing the bandwidth of sparse symmetric matrices
inferredcites →https://doi.org/10.21136/cmj.1970.100949openalex-snapshot
A remark on a problem of Harary
inferredcites →https://doi.org/10.2140/pjm.1965.15.835openalex-snapshot
Incidence matrices and interval graphs
inferredcites →https://doi.org/10.2307/2287146openalex-snapshot
The Theory and Applications of Graphs.
inferredcites →https://doi.org/10.2307/2333777openalex-snapshot
The Theory of Graphs and its Applications.
inferredcites →https://doi.org/10.2514/3.4575openalex-snapshot
An automatic node-relabeling scheme for bandwidth minimization of stiffness matrices.
inferredcites →https://doi.org/10.2514/3.55465openalex-snapshot
Comment on "An Automatic Node-Relabeling Scheme for Bandwidth Minimization of Stiffness Matrices"
inferredcites →https://doi.org/10.2514/3.55466openalex-snapshot
Reply by Author to J. Barlow and C.G. Marples
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
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A survey of solved problems and applications on bandwidth, edgesum, and profile of graphs
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An extremal bandwidth problem for bipartite graphs
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Note: On the set-union knapsack problem
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Laplace eigenvalues and bandwidth‐type invariants of graphs
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Maximum Bandwidth Under Edge Addition
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A compilation of relations between graph invariants
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On the separation number of a graph
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Node and element resequencing using the Laplacian of a finite element graph: Part I—General concepts and algorithm
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Bandwidth reduction by simulated annealing
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Approximating the Bandwidth for Asteroidal Triple-Free Graphs
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Approximating Layout Problems on Random Geometric Graphs
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Parallel Multigrid Preconditioning of the Conjugate Gradient Method for Systems of Subsurface Hydrology
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Approximating the Bandwidth via Volume Respecting Embeddings
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Optimal Embedding of Complete Binary Trees into Lines and Grid
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Interval Completion with the Smallest Max-Degree
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Graph Bandwidth of Weighted Caterpillars
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Approximating the Bandwidth of Caterpillars
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Minimal numberings of the vertices of trees — Approximate approach
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Bandwidth of Split and Circular Permutation Graphs
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A New Measure for the Bandwidth Minimization Problem
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Reordering the Reorderable Matrix as an Algorithmic Problem
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Coping with the NP-Hardness of the Graph Bandwidth Problem
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Labeling Schemes for Weighted Dynamic Trees
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On the Monotonicity of Games Generated by Symmetric Submodular Functions
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Approximating Bandwidth by Mixing Layouts of Interval Graphs
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Bandwidth and profile minimization
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Approximation algorithms for the Bandwidth Minimization Problem for a large class of trees
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Optimal embedding of a toroidal array in a linear array
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Optimal embedding of complete binary trees into lines and grids
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Book embeddings and crossing numbers
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Approximating the bandwidth for asteroidal triple-free graphs
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Polynomial time approximation schemes for some dense instances of NP-hard optimization problems
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Ultrafast randomized parallel construction and approximation algorithms for spanning forests in dense graphs
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A Hyper-Heuristic Approach to Evolving Algorithms for Bandwidth Reduction Based on Genetic Programming
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Ultrafast Randomized Parallel Construction- and Approximation Algorithms for Spanning Forests in Dense Graphs
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Eigenvalues in Combinatorial Optimization
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SDP Relaxations for Some Combinatorial Optimization Problems
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Optimal Grid Drawings of Complete Multipartite Graphs and an Integer Variant of the Algebraic Connectivity
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Brain Storm Optimization Algorithms for Solving Equations Systems
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Improved Lower Bounds for the Cyclic Bandwidth Problem
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On the Queue Number of Planar Graphs
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The Rique-Number of Graphs
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On the Parameterized Complexity of the Structure of Lineal Topologies (Depth-First Spanning Trees) of Finite Graphs: The Number of Leaves
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Ordering Transactions with Bounded Unfairness: Definitions, Complexity and Constructions
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Best of Both Worlds: Solving the Cyclic Bandwidth Problem by Combining Pre-existing Knowledge and Constraint Programming Techniques
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A Multi-centrality Heuristic for the Bandwidth Reduction Problem
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On the Rique Number of Series-Parallel Graphs and Planar Bipartite Graphs
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On the Complexity of Constrained Reconfiguration and Motion Planning
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Bandwidth of Nondeterministic Finite Automata
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Using ILP/SAT to Determine Pathwidth, Visibility Representations, and other Grid-Based Graph Drawings
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Linear Layout Problems
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A Generalization of the Directed Graph Layering Problem
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An Annotated Glossary of Graph Theory Parameters, with Conjectures
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Improving the Performance of a Genetic Algorithm Using a Variable-Reordering Algorithm
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Alphabet Permutation for Differentially Encoding Text
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An Improved Evaluation Function for the Bandwidth Minimization Problem
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Graph Searching, Elimination Trees, and a Generalization of Bandwidth
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Two Pages Graph Layout Via Recurrent Multivalued Neural Networks
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K-Pages Graph Drawing with Multivalued Neural Networks
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Multilevel Bandwidth and Radio Labelings of Graphs
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Complexity and Algorithms for Well-Structured k-SAT Instances
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Graph Layout Problems Parameterized by Vertex Cover
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Bandwidth of Bipartite Permutation Graphs
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Random Generation and Enumeration of Proper Interval Graphs
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Counting Subgraphs via Homomorphisms
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Natural Parameter Values for Generalized Gene Adjacency
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Thread Graphs, Linear Rank-Width and Their Algorithmic Applications
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Bandwidth and Low Dimensional Embedding
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Subexponential Parameterized Algorithm for Computing the Cutwidth of a Semi-complete Digraph
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Numberings on Graphs Having Small Edge Weights
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Parameterized Complexity of Bandwidth on Trees
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Sequences of Radius k for Complete Bipartite Graphs
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Embedding one Interconnection Network in Another
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A Multi-start Variable Neighborhood Tabu Search Algorithm for the Cyclic Bandwidth Problem
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Profile minimization problem for matrices and graphs
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On upper bounds of bandwidths of trees
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Bandwidth Minimization: An approximation algorithm for caterpillars
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Approximation algorithms for the bandwidth minimization problem for a large class of trees
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Comparing interconnection networks
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A Parameterized Complexity View on Collapsing k-Cores
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New Classes of Extremal Graphs with Given Bandwidth
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Graph Searching, Elimination Trees, and a Generalization of Bandwidth
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Approximating the Bandwidth of Caterpillars
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An Improved Upper Bound on the Queue Number of Planar Graphs
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Bandwidth Parameterized by Cluster Vertex Deletion Number
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Finding Exact Solutions to the Bandwidth Minimization Problem
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On the solution of the graph bandwidth problem by means of search methods
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On effective and efficient graph edge labeling
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An analysis of some linear graph layout heuristics
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A Characterisation of Posets that Are nearly Antichains
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Bandwidth of WK-recursive networks and its sparse matrix computation
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A degree sequence method for the cutwidth problem of graphs
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Graphs of Small Bandwidth and the Firefighter Problem
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The bandwidth problem and operations on graphs
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Graphs with small bandwidth and cutwidth
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On the size of graphs of a given bandwidth
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Bandwidth of theta graphs with short paths
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On bandwidth and edgesum for the composition of two graphs
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The bandwidth of a tree with k leaves is at most [k2]
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A short proof of the dilation of a toroidal mesh in a path
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On embedding graphs in trees
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Optimal linear labelings and eigenvalues of graphs
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Decompositions into linear forests and difference labelings of graphs
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NP-completeness for minimizing maximum edge length in grid embeddings
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Bandwidth constrained NP-complete problems
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Linear graph grammars: Power and complexity
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Investigation of the structure of binary variables
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Algorithms for numbering the nodes of finite-element meshes
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An ant colony hyperheuristic approach for matrix bandwidth reduction
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Reinforcement learning driven heuristic for two-dimensional bandwidth minimization
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Lower bounds for the bandwidth problem
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Approximating the fixed linear crossing number
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The profile of the Cartesian product of graphs
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On explicit formulas for bandwidth and antibandwidth of hypercubes
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Obstructions for linear rank-width at most 1
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Sequences of radius k for complete bipartite graphs
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Minimum degree conditions for the strength and bandwidth of graphs
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Intersection models and forbidden pattern characterizations for 2-thin and proper 2-thin graphs
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Bandwidth of the strong product of two connected graphs
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Bandwidth of the corona of two graphs
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Degree bounds for linear discrepancy of interval orders and disconnected posets
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Bandwidth and pathwidth of three-dimensional grids
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Bandwidth of trees of diameter at most 4
inferred← citeshttps://doi.org/10.1016/j.disc.2014.04.029openalex-snapshot
Cutwidth of triangular grids
inferred← citeshttps://doi.org/10.1016/j.ejor.2005.02.066openalex-snapshot
Heuristics for matrix bandwidth reduction
inferred← citeshttps://doi.org/10.1016/j.ejor.2005.12.052openalex-snapshot
An improved simulated annealing algorithm for bandwidth minimization
inferred← citeshttps://doi.org/10.1016/j.ejor.2008.12.015openalex-snapshot
Variable neighbourhood search for bandwidth reduction
inferred← citeshttps://doi.org/10.1016/j.ejor.2009.09.017openalex-snapshot
The minimization of open stacks problem: A review of some properties and their use in pre-processing operations
inferred← citeshttps://doi.org/10.1016/j.endm.2005.06.062openalex-snapshot
Edge Addition Number of Cartesian Product of Paths and Cycles
inferred← citeshttps://doi.org/10.1016/j.eswa.2025.127986openalex-snapshot
Two dimensional bandwidth minimization problem using a novel evaluation function
inferred← citeshttps://doi.org/10.1016/j.ic.2007.08.004openalex-snapshot
Labeling schemes for weighted dynamic trees
inferred← citeshttps://doi.org/10.1016/j.ipl.2003.12.004openalex-snapshot
On the profile of the corona of two graphs
inferred← citeshttps://doi.org/10.1016/j.ipl.2010.04.013openalex-snapshot
Two models of two-dimensional bandwidth problems
inferred← citeshttps://doi.org/10.1016/j.jcss.2010.06.006openalex-snapshot
Hardness results for approximating the bandwidth
inferred← citeshttps://doi.org/10.1016/j.jcss.2025.103680openalex-snapshot
On the parameterized complexity of lineal topologies (depth-first spanning trees) with many or few leaves
inferred← citeshttps://doi.org/10.1016/j.jctb.2019.01.006openalex-snapshot
On width measures and topological problems on semi-complete digraphs
inferred← citeshttps://doi.org/10.1016/j.jphysparis.2012.01.001openalex-snapshot
Markov models for fMRI correlation structure: Is brain functional connectivity small world, or decomposable into networks?
inferred← citeshttps://doi.org/10.1016/j.orl.2011.08.005openalex-snapshot
A bandwidth reduction algorithm for L-shaped and Z-shaped grid structured graphs
inferred← citeshttps://doi.org/10.1016/j.tcs.2006.01.046openalex-snapshot
On the edge-bandwidth of graph products
inferred← citeshttps://doi.org/10.1016/j.tcs.2006.06.018openalex-snapshot
Edge-bandwidth of grids and tori
inferred← citeshttps://doi.org/10.1016/j.tcs.2006.07.015openalex-snapshot
Graph bandwidth of weighted caterpillars
inferred← citeshttps://doi.org/10.1016/j.tcs.2007.03.012openalex-snapshot
An extremal graph with given bandwidth
inferred← citeshttps://doi.org/10.1016/j.tcs.2008.07.029openalex-snapshot
On the bandwidth of 3-dimensional Hamming graphs
inferred← citeshttps://doi.org/10.1016/j.tcs.2013.05.038openalex-snapshot
Bandwidth and low dimensional embedding
inferred← citeshttps://doi.org/10.1016/j.tcs.2022.07.036openalex-snapshot
The mixed page number of graphs
inferred← citeshttps://doi.org/10.1016/s0012-365x(00)00379-4openalex-snapshot
Characterization of graphs with equal bandwidth and cyclic bandwidth
inferred← citeshttps://doi.org/10.1016/s0012-365x(01)00091-7openalex-snapshot
On approximating the maximum diameter ratio of graphs
inferred← citeshttps://doi.org/10.1016/s0012-365x(01)00455-1openalex-snapshot
Bandwidth of the cartesian product of two connected graphs
inferred← citeshttps://doi.org/10.1016/s0012-365x(03)00131-6openalex-snapshot
Bandwidth of the composition of two graphs
inferred← citeshttps://doi.org/10.1016/s0012-365x(97)00040-xopenalex-snapshot
Harper-type lower bounds and the bandwidths of the compositions of graphs
inferred← citeshttps://doi.org/10.1016/s0012-365x(97)00063-0openalex-snapshot
On the bandwidth of convex triangulation meshes
inferred← citeshttps://doi.org/10.1016/s0012-365x(98)00009-0openalex-snapshot
Bandwidth and density for block graphs
inferred← citeshttps://doi.org/10.1016/s0166-218x(01)00220-7openalex-snapshot
Bandwidth and topological bandwidth of graphs with few P4's
inferred← citeshttps://doi.org/10.1016/s0166-218x(01)00314-6openalex-snapshot
Algorithms for the fixed linear crossing number problem
inferred← citeshttps://doi.org/10.1016/s0166-218x(02)00389-xopenalex-snapshot
On the domination search number
inferred← citeshttps://doi.org/10.1016/s0166-218x(02)00459-6openalex-snapshot
On the monotonicity of games generated by symmetric submodular functions
inferred← citeshttps://doi.org/10.1016/s0166-218x(02)00574-7openalex-snapshot
Interval degree and bandwidth of a graph
inferred← citeshttps://doi.org/10.1016/s0166-218x(03)00298-1openalex-snapshot
Algorithms for graphs with small octopus
inferred← citeshttps://doi.org/10.1016/s0166-218x(95)00005-copenalex-snapshot
On bandwidth for the tensor product of paths and cycles
inferred← citeshttps://doi.org/10.1016/s0166-218x(97)00041-3openalex-snapshot
Characterizations and algorithmic applications of chordal graph embeddings
inferred← citeshttps://doi.org/10.1016/s0166-218x(97)00131-5openalex-snapshot
Helicopter search problems, bandwidth and pathwidth
inferred← citeshttps://doi.org/10.1016/s0167-5060(08)70455-2openalex-snapshot
Bandwidth versus Bandsize
inferred← citeshttps://doi.org/10.1016/s0167-5060(08)70571-5openalex-snapshot
Graphs with Small Bandwidth and Cutwidth
inferred← citeshttps://doi.org/10.1016/s0167-6377(98)00040-6openalex-snapshot
A new matrix bandwidth reduction algorithm
inferred← citeshttps://doi.org/10.1016/s0304-0208(08)72457-5openalex-snapshot
The Bandwidth Problem: critical Subgraphs and the Solution for Caterpillars
inferred← citeshttps://doi.org/10.1016/s0304-0208(08)73443-1openalex-snapshot
On the Bandwidth of Random Graphs
inferred← citeshttps://doi.org/10.1016/s0304-3975(00)00068-2openalex-snapshot
Bounding the bandwidths for graphs
inferred← citeshttps://doi.org/10.1016/s0304-3975(03)00052-5openalex-snapshot
On the bandwidth of a Hamming graph
inferred← citeshttps://doi.org/10.1016/s0304-3975(03)00234-2openalex-snapshot
New results on edge-bandwidth
inferred← citeshttps://doi.org/10.1016/s0304-3975(03)00238-xopenalex-snapshot
The bandwidth minimization problem for cyclic caterpillars with hair length 1 is NP-complete
inferred← citeshttps://doi.org/10.1016/s0304-3975(99)00181-4openalex-snapshot
Semi-definite relaxations for minimum bandwidth and other vertex-ordering problems
inferred← citeshttps://doi.org/10.1016/s0362-546x(97)00344-1openalex-snapshot
Systolic bandwidth and profile reduction of sparse matrices on pipenets
inferred← citeshttps://doi.org/10.1016/s0377-2217(02)00715-4openalex-snapshot
GRASP and path relinking for the matrix bandwidth minimization
inferred← citeshttps://doi.org/10.1016/s1571-0653(05)00747-xopenalex-snapshot
Approximating Bandwidth by Mixing Layouts of Interval Graphs
inferred← citeshttps://doi.org/10.1016/s1571-0653(05)80035-6openalex-snapshot
Approximating Bandwidth by Mixing Layouts of Interval Graphs
inferred← citeshttps://doi.org/10.1023/a:1012219816274openalex-snapshot
Linear Discrepancy and Weak Discrepancy of Partially Ordered Sets
inferred← citeshttps://doi.org/10.1023/b:cmaj.0000042378.90480.b1openalex-snapshot
On Harpers' Result Concerning the Bandwidths of Graphs
inferred← citeshttps://doi.org/10.1049/wss2.12074openalex-snapshot
Exploiting sparsity for localisation of large‐scale wireless sensor networks
inferred← citeshttps://doi.org/10.1051/ita/1993270504651openalex-snapshot
Congestion optimale du plongement de l’hypercube $H (n)$ dans la chaîne $P(2^n)$
inferred← citeshttps://doi.org/10.1051/ita/1995290604871openalex-snapshot
On bandwidth, cutwidth, and quotient graphs
inferred← citeshttps://doi.org/10.1051/ita/2011120openalex-snapshot
Square-root rule of two-dimensional bandwidth problem
inferred← citeshttps://doi.org/10.1051/ita/2014027openalex-snapshot
New bounds on the edge-bandwidth of triangular grids
inferred← citeshttps://doi.org/10.1080/00207168408803418openalex-snapshot
A general strategy on the bandwidth minimization (BM) problem
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