Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
The steiner problem with edge lengths 1 and 2,
Information Processing Letters
SIAM Journal on Computing
Analyzing the Held-Karp TSP bound: a monotonicity property with application
Information Processing Letters
Euclidean minimum spanning trees and bichromatic closest pairs
Discrete & Computational Geometry
Approximating clique is almost NP-complete (preliminary version)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
The complexity of the Lin-Kernighan heuristic for the traveling salesman problem
SIAM Journal on Computing
Worst-case comparison of valid inequalities for the TSP
Mathematical Programming: Series A and B
Approximation algorithms for geometric tour and network design problems (extended abstract)
Proceedings of the eleventh annual symposium on Computational geometry
A constant-factor approximation for the k-MST problem in the plane
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
Approximation algorithms for geometric problems
Approximation algorithms for NP-hard problems
When Hamming meets Euclid: the approximability of geometric TSP and MST (extended abstract)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Faster geometric k-point MST approximation
Computational Geometry: Theory and Applications
Approximation schemes for Euclidean k-medians and related problems
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Approximating geometrical graphs via “spanners” and “banyans”
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
New results on the old k-opt algorithm for the TSP
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
A polynomial-time approximation scheme for weighted planar graph TSP
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Journal of the ACM (JACM)
P-Complete Approximation Problems
Journal of the ACM (JACM)
Low-Degree Spanning Trees of Small Weight
SIAM Journal on Computing
Parallel Construction of Quadtrees and Quality Triangulations
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
An approximation scheme for planar graph TSP
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Some NP-complete geometric problems
STOC '76 Proceedings of the eighth annual ACM symposium on Theory of computing
Finding Cuts in the TSP (A preliminary report)
Finding Cuts in the TSP (A preliminary report)
A 3-approximation for the minimum tree spanning k vertices
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Polynomial time approximation schemes for Euclidean TSP and other geometric problems
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Better approximation bounds for the network and Euclidean Steiner tree problems
Better approximation bounds for the network and Euclidean Steiner tree problems
Approximation schemes for minimum latency problems
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
On approximability of the minimum-cost k-connected spanning subgraph problem
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
A 2 + ε approximation algorithm for the k-MST problem
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for TSP with neighborhoods in the plane
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Statistical mechanics methods and phase transitions in optimizationproblems
Theoretical Computer Science - Phase transitions in combinatorial problems
ACM SIGACT News
Scheduling and caching strategies for correlated data in push-based information systems
ACM SIGAPP Applied Computing Review
Minimum-buffered routing of non-critical nets for slew rate and reliability control
Proceedings of the 2001 IEEE/ACM international conference on Computer-aided design
Competitive on-line coverage of grid environments by a mobile robot
Computational Geometry: Theory and Applications
Efficient Steiner tree construction based on spanning graphs
Proceedings of the 2003 international symposium on Physical design
Embeddings and non-approximability of geometric problems
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation Algorithms for the Minimum Bends Traveling Salesman Problem
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
Fast Approximation Schemes for Euclidean Multi-connectivity Problems
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Towards a Predictive Computational Complexity Theory
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Polynomial-Time Approximation Schemes for the Euclidean Survivable Network Design Problem
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Approximate TSP in Graphs with Forbidden Minors
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
A Simple and Quick Approximation Algorithm for Traveling Salesman Problem in the Plane
ISAAC '00 Proceedings of the 11th International Conference on Algorithms and Computation
Tree-Approximations for the Weighted Cost-Distance Problem
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
An FPTAS for Weight-Constrained Steiner Trees in Series-Parallel Graphs
COCOON '01 Proceedings of the 7th Annual International Conference on Computing and Combinatorics
Approximation Schemes for Geometric NP-Hard Problems: A Survey
FST TCS '01 Proceedings of the 21st Conference on Foundations of Software Technology and Theoretical Computer Science
TSP with Neighborhoods of Varying Size
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
CIAC '00 Proceedings of the 4th Italian Conference on Algorithms and Complexity
On Salesmen, Repairmen, Spiders, and Other Traveling Agents
CIAC '00 Proceedings of the 4th Italian Conference on Algorithms and Complexity
Euclidean bounded-degree spanning tree ratios
Proceedings of the nineteenth annual symposium on Computational geometry
Polynomial-time approximation schemes for packing and piercing fat objects
Journal of Algorithms
The geometric maximum traveling salesman problem
Journal of the ACM (JACM)
A PTAS for weight constrained Steiner trees in series-parallel graphs
Theoretical Computer Science
Neural Networks - 2003 Special issue: Advances in neural networks research IJCNN'03
Journal of Experimental Algorithmics (JEA)
Approximation schemes for minimum 2-edge-connected and biconnected subgraphs in planar graphs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
The Steiner ratio of high-dimensional BanachMinkowski spaces
Discrete Applied Mathematics - Optimal discrete structure and algorithms (ODSA 2000)
Approximation algorithms for TSP with neighborhoods in the plane
Journal of Algorithms - Special issue: Twelfth annual ACM-SIAM symposium on discrete algorithms
Bypassing the embedding: algorithms for low dimensional metrics
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
On coresets for k-means and k-median clustering
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Approximation algorithms for network design with metric costs
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Saving an epsilon: a 2-approximation for the k-MST problem in graphs
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Deploying sensor networks with guaranteed capacity and fault tolerance
Proceedings of the 6th ACM international symposium on Mobile ad hoc networking and computing
Smaller coresets for k-median and k-means clustering
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Computing in Science and Engineering
The complexity of low-distortion embeddings between point sets
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
How fast is the k-means method?
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
The complexity of base station positioning in cellular networks
Discrete Applied Mathematics
A linear-time approximation scheme for planar weighted TSP
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Improved lower and upper bounds for universal TSP in planar metrics
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Efficient algorithms for online decision problems
Journal of Computer and System Sciences - Special issue: Learning theory 2003
TSP with neighborhoods of varying size
Journal of Algorithms
On the complexity of approximating tsp with neighborhoods and related problems
Computational Complexity
A quasi-polynomial time approximation scheme for minimum weight triangulation
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
A subset spanner for Planar graphs,: with application to subset TSP
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
The orienteering problem in the plane revisited
Proceedings of the twenty-second annual symposium on Computational geometry
Polynomial time approximation schemes and parameterized complexity
Discrete Applied Mathematics
Steiner Trees and 3-D Macromolecular Conformation
INFORMS Journal on Computing
On the Integrality Ratio for the Asymmetric Traveling Salesman Problem
Mathematics of Operations Research
Online Routing Problems: Value of Advanced Information as Improved Competitive Ratios
Transportation Science
Limitations of VCG-based mechanisms
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Region-restricted clustering for geographic data mining
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Good triangulations yield good tours
Computers and Operations Research
A PTAS for TSP with neighborhoods among fat regions in the plane
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
A polynomial-time approximation scheme for Steiner tree in planar graphs
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Worst case and probabilistic analysis of the 2-Opt algorithm for the TSP: extended abstract
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Approximate distance oracles for geometric spanners
ACM Transactions on Algorithms (TALG)
Better mechanisms for combinatorial auctions via maximal-in-range algorithms?
ACM SIGecom Exchanges
Approximating TSP on metrics with bounded global growth
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Rendezvous design algorithms for wireless sensor networks with a mobile base station
Proceedings of the 9th ACM international symposium on Mobile ad hoc networking and computing
Approximating k-hop minimum spanning trees in Euclidean metrics
Information Processing Letters
Approximation algorithms for a facility location problem with service capacities
ACM Transactions on Algorithms (TALG)
Minimum Spanning Tree with Neighborhoods
AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
Efficient Algorithms for Fixed-Precision Instances of Bin Packing and Euclidean TSP
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Faster Steiner Tree Computation in Polynomial-Space
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
An Iterated Local Search Approach for Finding Provably Good Solutions for Very Large TSP Instances
Proceedings of the 10th international conference on Parallel Problem Solving from Nature: PPSN X
Improved Approximation Ratios for Traveling Salesperson Tours and Paths in Directed Graphs
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Hardness of Embedding Metric Spaces of Equal Size
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Region-restricted clustering for geographic data mining
Computational Geometry: Theory and Applications
Light orthogonal networks with constant geometric dilation
Journal of Discrete Algorithms
Approximating the Metric TSP in Linear Time
Graph-Theoretic Concepts in Computer Science
Degree-bounded minimum spanning trees
Discrete Applied Mathematics
A quasi-polynomial time approximation scheme for minimum weight triangulation
Journal of the ACM (JACM)
Not being (super)thin or solid is hard: A study of grid Hamiltonicity
Computational Geometry: Theory and Applications
An O(n log n) approximation scheme for Steiner tree in planar graphs
ACM Transactions on Algorithms (TALG)
The Euclidean degree-4 minimum spanning tree problem is NP-hard
Proceedings of the twenty-fifth annual symposium on Computational geometry
Approximation algorithms for maximum independent set of pseudo-disks
Proceedings of the twenty-fifth annual symposium on Computational geometry
The status of the P versus NP problem
Communications of the ACM - The Status of the P versus NP Problem
Fast minimum-weight double-tree shortcutting for metric TSP: Is the best one good enough?
Journal of Experimental Algorithmics (JEA)
Hard constraint satisfaction problems have hard gaps at location 1
Theoretical Computer Science
Approximating the minimum weight spanning tree of a set of points in the Hausdorff metric
Computational Geometry: Theory and Applications
Approximation Algorithms for Buy-at-Bulk Geometric Network Design
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Communications of the ACM
Linear-time approximation schemes for clustering problems in any dimensions
Journal of the ACM (JACM)
A near linear time approximation scheme for Steiner tree among obstacles in the plane
Computational Geometry: Theory and Applications
On Euclidean vehicle routing with allocation
Computational Geometry: Theory and Applications
PTAS for k-Tour Cover Problem on the Plane for Moderately Large Values of k
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
The complexity of base station positioning in cellular networks
Discrete Applied Mathematics
The Steiner ratio of high-dimensional Banach-Minkowski spaces
Discrete Applied Mathematics
An annotated bibliography of combinatorial optimization problems with fixed cardinality constraints
Discrete Applied Mathematics - Special issue: 2nd cologne/twente workshop on graphs and combinatorial optimization (CTW 2003)
TSP with neighborhoods of varying size
Journal of Algorithms
Traveling salesman problem of segments
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
Approximation schemes for degree-restricted MST and red-blue separation problem
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Rotational steiner ratio problem under uniform orientation metrics
CJCDGCGT'05 Proceedings of the 7th China-Japan conference on Discrete geometry, combinatorics and graph theory
Fast minimum-weight double-tree shortcutting for metric TSP
WEA'07 Proceedings of the 6th international conference on Experimental algorithms
Approximating TSP solution by MST based graph pyramid
GbRPR'07 Proceedings of the 6th IAPR-TC-15 international conference on Graph-based representations in pattern recognition
Using mobile robots to harvest data from sensor fields
IEEE Wireless Communications
Probabilistic analysis of the degree bounded minimum spanning tree problem
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
Understanding planning tasks: domain complexity and heuristic decomposition
Understanding planning tasks: domain complexity and heuristic decomposition
Self-organization and evolution combined to address the vehicle routing problem
EA'07 Proceedings of the Evolution artificielle, 8th international conference on Artificial evolution
Approximation schemes for steiner forest on planar graphs and graphs of bounded treewidth
Proceedings of the forty-second ACM symposium on Theory of computing
An improved LP-based approximation for steiner tree
Proceedings of the forty-second ACM symposium on Theory of computing
Theoretical Computer Science
Better bounds on the union complexity of locally fat objects
Proceedings of the twenty-sixth annual symposium on Computational geometry
Proceedings of the twenty-sixth annual symposium on Computational geometry
Deploying sensor networks with guaranteed fault tolerance
IEEE/ACM Transactions on Networking (TON)
A quasi-polynomial time approximation scheme for Euclidean capacitated vehicle routing
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Racetrack: an approximation algorithm for the mobile sink routing problem
ADHOC-NOW'10 Proceedings of the 9th international conference on Ad-hoc, mobile and wireless networks
Algorithmics in intensity-modulated radiation therapy
Algorithms and theory of computation handbook
Approximation algorithms for NP-hard optimization problems
Algorithms and theory of computation handbook
Improved lower bounds for the universal and a priori TSP
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Algorithm engineering: bridging the gap between algorithm theory and practice
Algorithm engineering: bridging the gap between algorithm theory and practice
Fast track article: Designing hierarchical sensor networks with mobile data collectors
Pervasive and Mobile Computing
Stochastic minimum spanning trees in euclidean spaces
Proceedings of the twenty-seventh annual symposium on Computational geometry
On the euclidean bottleneck full Steiner tree problem
Proceedings of the twenty-seventh annual symposium on Computational geometry
Improved approximations for hard optimization problems via problem instance classification
Rainbow of computer science
Polynomial area bounds for MST embeddings of trees
Computational Geometry: Theory and Applications
Capacitated vehicle routing with non-uniform speeds
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Dealing with large hidden constants: engineering a planar steiner tree PTAS
Journal of Experimental Algorithmics (JEA)
Approximation schemes for capacitated geometric network design
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Clique clustering yields a PTAS for max-coloring interval graphs
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Approximation Schemes for Steiner Forest on Planar Graphs and Graphs of Bounded Treewidth
Journal of the ACM (JACM)
On the area requirements of Euclidean minimum spanning trees
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
PTAS for densest k-subgraph in interval graphs
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Exploring and triangulating a region by a swarm of robots
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Staying-alive path planning with energy optimization for mobile robots
Expert Systems with Applications: An International Journal
The effect of the asymmetry of road transportation networks on the traveling salesman problem
Computers and Operations Research
Interpolating an unorganized 2D point cloud with a single closed shape
Computer-Aided Design
Approximation of octilinear steiner trees constrained by hard and soft obstacles
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Approximation algorithms for euclidean group TSP
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Efficient approximation schemes for geometric problems?
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Geometric network design with selfish agents
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Simple distributed algorithms for approximating minimum steiner trees
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Euclidean prize-collecting steiner forest
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Randomized rounding for routing and covering problems: experiments and improvements
SEA'10 Proceedings of the 9th international conference on Experimental Algorithms
Geometric minimum spanning trees with GEOFILTERKRUSKAL*
SEA'10 Proceedings of the 9th international conference on Experimental Algorithms
Hardness and approximation of octilinear steiner trees
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Approximation algorithms for network design and facility location with service capacities
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Approximation schemes for node-weighted geometric steiner tree problems
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Pricing on paths: a PTAS for the highway problem
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
The asymmetric traveling salesman problem on graphs with bounded genus
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Probabilistic analysis for a multiple depot vehicle routing problem
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
On the vehicle routing problem
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
Capacitated max -batching with interval graph compatibilities
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
On approximating the TSP with intersecting neighborhoods
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Shape rectangularization problems in intensity-modulated radiation therapy
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
An improved strategy for exploring a grid polygon
SIROCCO'09 Proceedings of the 16th international conference on Structural Information and Communication Complexity
Reconfigurations in graphs and grids
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
A modified inver-over operator for the traveling salesman problem
ICIC'11 Proceedings of the 7th international conference on Advanced Intelligent Computing Theories and Applications: with aspects of artificial intelligence
Efficient data collection from wireless nodes under the two-ring communication model
International Journal of Robotics Research
A near-linear time ε-approximation algorithm for geometric bipartite matching
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
The traveling salesman problem: low-dimensionality implies a polynomial time approximation scheme
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
The Traveling Salesman Problem with flexible coloring
Discrete Applied Mathematics
The traveling salesman problem with few inner points
Operations Research Letters
Research paper: The saga of minimum spanning trees
Computer Science Review
An improved algorithm for computing Steiner minimal trees in Euclidean d-space
Discrete Optimization
Computers & Mathematics with Applications
An improved upper bound for the TSP in cubic 3-edge-connected graphs
Operations Research Letters
Shifting strategy for geometric graphs without geometry
Journal of Combinatorial Optimization
Technical Note---Approximation Algorithms for VRP with Stochastic Demands
Operations Research
Growing half-balls: minimizing storage and communication costs in CDNs
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
On approximating string selection problems with outliers
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
A probabilistic analysis of christofides' algorithm
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
A near linear time approximation scheme for steiner tree among obstacles in the plane
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
On euclidean vehicle routing with allocation
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
A new light-based solution to the Hamiltonian path problem
Future Generation Computer Systems
Combinatorial complexity problem reduction by the use of artificial vaccines
Expert Systems with Applications: An International Journal
Computing the variance of tour costs over the solution space of the TSP in polynomial time
Computational Optimization and Applications
LION'12 Proceedings of the 6th international conference on Learning and Intelligent Optimization
Steiner Tree Approximation via Iterative Randomized Rounding
Journal of the ACM (JACM)
Geometric conditions for Euclidean Steiner trees in Rd
Computational Geometry: Theory and Applications
Proceedings of the twelfth workshop on Foundations of genetic algorithms XII
Fast hamiltonicity checking via bases of perfect matchings
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
On the approximability of Dense Steiner Problems
Journal of Discrete Algorithms
On approximating string selection problems with outliers
Theoretical Computer Science
Exponential approximation schemata for some network design problems
Journal of Discrete Algorithms
On the area requirements of Euclidean minimum spanning trees
Computational Geometry: Theory and Applications
Annals of Mathematics and Artificial Intelligence
A Survey of Parallel and Distributed Algorithms for the Steiner Tree Problem
International Journal of Parallel Programming
Hi-index | 0.03 |
We present a polynomial time approximation scheme for Euclidean TSP in fixed dimensions. For every fixed c 1 and given any n nodes in R 2, a randomized version of the scheme finds a (1 + 1/c)-approximation to the optimum traveling salesman tour in O(n(log n)O(c)) time. When the nodes are in R d, the running time increases to O(n(log n)(O(d c))d-1). For every fixed c, d the running time is n • poly(logn), that is nearly linear in n. The algorithmm can be derandomized, but this increases the running time by a factor O(nd). The previous best approximation algorithm for the problem (due to Christofides) achieves a 3/2-aproximation in polynomial time.We also give similar approximation schemes for some other NP-hard Euclidean problems: Minimum Steiner Tree, k-TSP, and k-MST. (The running times of the algorithm for k-TSP and k-MST involve an additional multiplicative factor k.) The previous best approximation algorithms for all these problems achieved a constant-factor approximation. We also give efficient approximation schemes for Euclidean Min-Cost Matching, a problem that can be solved exactly in polynomial time.All our algorithms also work, with almost no modification, when distance is measured using any geometric norm (such as ℓ p for p ≥ 1 or other Minkowski norms). They also have simple parallel (i.e., NC) implementations.