A unified approach to domination problems on interval graphs
Information Processing Letters
Ordering problems approximated: single-processor scheduling and interval graph completion
Proceedings of the 18th international colloquium on Automata, languages and programming
Cut problems and their application to divide-and-conquer
Approximation algorithms for NP-hard problems
Approximation algorithms for Steiner and directed multicuts
Journal of Algorithms
A network flow approach for hierarchical tree partitioning
DAC '97 Proceedings of the 34th annual Design Automation Conference
How Good is Recursive Bisection?
SIAM Journal on Scientific Computing
An O(log k) Approximate Min-Cut Max-Flow Theorem and Approximation Algorithm
SIAM Journal on Computing
Approximating the bandwidth via volume respecting embeddings (extended abstract)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Semi-definite relaxations for minimum bandwidth and other vertex-ordering problems
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
New approximation techniques for some ordering problems
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Fast Approximate Graph Partitioning Algorithms
SIAM Journal on Computing
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
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Approximate Max-Flow Min-(Multi)Cut Theorems and Their Applications
SIAM Journal on Computing
Divide-and-conquer approximation algorithms via spreading metrics
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Random Projection: A New Approach to VLSI Layout
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
A survey of graph layout problems
ACM Computing Surveys (CSUR)
Polylogarithmic inapproximability
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
The directed circular arrangement problem
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the sixteenth annual ACM symposium on Parallelism in algorithms and architectures
Improved approximation algorithms for minimum-weight vertex separators
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Improved lower and upper bounds for universal TSP in planar metrics
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
l22 spreading metrics for vertex ordering problems
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Advances in metric embedding theory
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Integrality gaps for sparsest cut and minimum linear arrangement problems
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
New theoretical results on quadratic placement
Integration, the VLSI Journal
An improved approximation ratio for the minimum linear arrangement problem
Information Processing Letters
Memory management optimization problems for integrated circuit simulators
Discrete Applied Mathematics
A divide and conquer algorithm for d-dimensional arrangement
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Cutting cycles of rods in space: hardness and approximation
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Partitioning graphs into balanced components
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
FPGA placement using space-filling curves: Theory meets practice
ACM Transactions on Embedded Computing Systems (TECS)
A linear-time algorithm to find a separator in a graph excluding a minor
ACM Transactions on Algorithms (TALG)
Fast unified floorplan topology generation and sizing on heterogeneous FPGAs
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
The directed circular arrangement problem
ACM Transactions on Algorithms (TALG)
On approximation of new optimization methods for assessing network vulnerability
INFOCOM'10 Proceedings of the 29th conference on Information communications
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
Decorous Lower Bounds for Minimum Linear Arrangement
INFORMS Journal on Computing
Revised GRASP with path-relinking for the linear ordering problem
Journal of Combinatorial Optimization
Multicommodity flows and cuts in polymatroidal networks
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Optimal linear arrangement of interval graphs
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Approximation algorithm for directed multicuts
WAOA'04 Proceedings of the Second international conference on Approximation and Online Algorithms
The feedback arc set problem with triangle inequality is a vertex cover problem
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Geometric quadrisection in linear time, with application to VLSI placement
Discrete Optimization
On new approaches of assessing network vulnerability: hardness and approximation
IEEE/ACM Transactions on Networking (TON)
Sorting noisy data with partial information
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
d-dimensional arrangement revisited
Information Processing Letters
Simplex partitioning via exponential clocks and the multiway cut problem
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We present a novel divide-and-conquer paradigm for approximating NP-hard graph optimization problems. The paradigm models graph optimization problems that satisfy two properties: First, a divide-and-conquer approach is applicable. Second, a fractional spreading metric is computable in polynomial time. The spreading metric assigns lengths to either edges or vertices of the input graph, such that all subgraphs for which the optimization problem is nontrivial have large diameters. In addition, the spreading metric provides a lower bound, t , on the cost of solving the optimization problem. We present a polynomial time approximation algorithm for problems modeled by our paradigm whose approximation factor is O(min{log t, log log t , log k log log k}) where k denotes the number of “interesting” vertices in the problem instance, and is at most the number of vertices. We present seven problems that can be formulated to fit the paradigm. For all these problems our algorithm improves previous results. The problems are: (1) linear arrangement; (2) embedding a graph in a d-dimensional mesh; (3) interval graph completion; (4) minimizing storage-time product; (5) subset feedback sets in directed graphs and multicuts in circular networks; (6) symmetric multicuts in directed networks; (7) balanced partitions and p-separators (for small values of p) in directed graphs.