Amortized efficiency of list update and paging rules
Communications of the ACM
Spacefilling curves and the planar travelling salesman problem
Journal of the ACM (JACM)
On-line Steiner trees in the Euclidean plane
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
The traveling salesman problem with distances one and two
Mathematics of Operations Research
Excluded minors, network decomposition, and multicommodity flow
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
On approximating arbitrary metrices by tree metrics
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Online computation and competitive analysis
Online computation and competitive analysis
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
Small distortion and volume preserving embeddings for planar and Euclidean metrics
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
A polynomial-time approximation scheme for weighted planar graph TSP
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
New approximation techniques for some ordering problems
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Divide-and-conquer approximation algorithms via spreading metrics
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Lectures on Discrete Geometry
Developments from a June 1996 seminar on Online algorithms: the state of the art
Developments from a June 1996 seminar on Online algorithms: the state of the art
Minimizing Congestion in General Networks
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
A polynomial-time tree decomposition to minimize congestion
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
Optimal oblivious routing in polynomial time
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
An approximation scheme for planar graph TSP
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Building Steiner trees with incomplete global knowledge
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Universal schemes for parallel communication
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Boosted sampling: approximation algorithms for stochastic optimization
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Approximating the Stochastic Knapsack Problem: The Benefit of Adaptivity
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Oblivious routing in directed graphs with random demands
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Universal approximations for TSP, Steiner tree, and set cover
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Oblivious routing on node-capacitated and directed graphs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
A linear-time approximation scheme for planar weighted TSP
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A constant approximation algorithm for the a priori traveling salesman problem
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
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
Stochastic minimum spanning trees in euclidean spaces
Proceedings of the twenty-seventh annual symposium on Computational geometry
Optimal lower bounds for universal and differentially private steiner trees and TSPs
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Algorithms for the universal and a priori TSP
Operations Research Letters
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A universal TSP tour of a metric space is a total ordering of the points of the space such that for any finite subset, the tour which visits these points in the given order is not too much longer than the optimal tour. There is a vast literature on the TSP problem, and universal TSP tours have been studied since the 1980's when Bartholdi and Platzman [29] introduced the spacefilling curve heuristic for the Euclidean TSP problem and conjectured that there exists a constant-competitive universal TSP tour based on this heuristic. Here, we settle this conjecture negatively by proving an Ω (6√log n/log log n) lower bound for universal TSP tours of the n × n grid; this is the first known example of a family of finite metrics with no constant-competitive universal tour.Generalizing from the n × n grid to arbitrary weighted planar graph metrics, and more generally H-minor-free metrics, we improve the best known upper bound for universal tours of such metrics from O(log4 n/ log log n) to O(log2 n).