Efficient parallel algorithms for edge coloring problems
Journal of Algorithms
A greedy approximation algorithm for constructing shortest common superstrings
Theoretical Computer Science - International Symposium on Mathematical Foundations of Computer Science, Bratisl
Approximation algorithms for the shortest common superstring problem
Information and Computation
An approximation algorithm for the asymmetric travelling salesman problem with distances one and two
Information Processing Letters
The traveling salesman problem with distances one and two
Mathematics of Operations Research
Linear approximation of shortest superstrings
Journal of the ACM (JACM)
Approximating Shortest Superstrings
SIAM Journal on Computing
Sequential and parallel approximation of shortest superstrings
Journal of Algorithms
Rotations of periodic strings and short superstrings
Journal of Algorithms
\boldmath A $2\frac12$-Approximation Algorithm for Shortest Superstring
SIAM Journal on Computing
Better approximations for max TSP
Information Processing Letters
A 7/8-approximation algorithm for metric Max TSP
Information Processing Letters
A new approximation algorithm for the asymmetric TSP with triangle inequality
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Improved Length Bounds for the Shortest Superstring Problem (Extended Abstract)
WADS '95 Proceedings of the 4th International Workshop on Algorithms and Data Structures
Two Approximation Algorithms for 3-Cycle Covers
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
A 2 2/3-Approximation Algorithm for the Shortest Superstring Problem
CPM '96 Proceedings of the 7th Annual Symposium on Combinatorial Pattern Matching
A simple algorithm for edge-coloring bipartite multigraphs
Information Processing Letters
A 5/8 Approximation Algorithm for the Maximum Asymmetric TSP
SIAM Journal on Discrete Mathematics
Journal of Computer and System Sciences
On the relationship between ATSP and the cycle cover problem
Theoretical Computer Science
Terminal backup, 3D matching, and covering cubic graphs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Improved algorithms for orienteering and related problems
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
A new approximation algorithm for the asymmetric TSP with triangle inequality
ACM Transactions on Algorithms (TALG)
Analysis of set-up time models: A metric perspective
Theoretical Computer Science
Approximating Multi-criteria Max-TSP
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
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
Minimum-weight cycle covers and their approximability
Discrete Applied Mathematics
An improved approximation algorithm for the ATSP with parameterized triangle inequality
Journal of Algorithms
A 2log2(n)-Approximation Algorithm for Directed Tour Cover
COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
Two Approximation Algorithms for ATSP with Strengthened Triangle Inequality
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
A 7/9 - Approximation Algorithm for the Maximum Traveling Salesman Problem
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Minimum-weight cycle covers and their approximability
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
An O(log n/ log log n)-approximation algorithm for the asymmetric traveling salesman problem
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Asymmetric traveling salesman path and directed latency problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
On shortest common superstring and swap permutations
SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
Deterministic algorithms for multi-criteria TSP
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Restricted common superstring and restricted common supersequence
CPM'11 Proceedings of the 22nd annual conference on Combinatorial pattern matching
Terminal Backup, 3D Matching, and Covering Cubic Graphs
SIAM Journal on Computing
Approximation algorithms for restricted cycle covers based on cycle decompositions
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
The asymmetric traveling salesman problem on graphs with bounded genus
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
On approximating multicriteria TSP
ACM Transactions on Algorithms (TALG)
Multi-Criteria TSP: min and max combined
WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
An O(log n) approximation ratio for the asymmetric traveling salesman path problem
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Approximation algorithms for multi-criteria traveling salesman problems
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
Improved approximation algorithms for metric maximum ATSP and maximum 3-cycle cover problems
Operations Research Letters
Approximation algorithms for maximum latency and partial cycle cover
Discrete Optimization
Deterministic algorithms for multi-criteria Max-TSP
Discrete Applied Mathematics
35/44-Approximation for asymmetric maximum TSP with triangle inequality
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
An improved integrality gap for asymmetric TSP paths
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
Improved inapproximability results for the shortest superstring and related problems
CATS '13 Proceedings of the Nineteenth Computing: The Australasian Theory Symposium - Volume 141
No-Wait flowshop scheduling is as hard as asymmetric traveling salesman problem
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Exponential approximation schemata for some network design problems
Journal of Discrete Algorithms
A probabilistic PTAS for shortest common superstring
Theoretical Computer Science
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A directed multigraph is said to be d-regular if the indegree and outdegree of every vertex is exactly d. By Hall's theorem, one can represent such a multigraph as a combination of at most n2 cycle covers, each taken with an appropriate multiplicity. We prove that if the d-regular multigraph does not contain more than ⌊d/2⌋ copies of any 2-cycle then we can find a similar decomposition into n2 pairs of cycle covers where each 2-cycle occurs in at most one component of each pair. Our proof is constructive and gives a polynomial algorithm to find such a decomposition. Since our applications only need one such a pair of cycle covers whose weight is at least the average weight of all pairs, we also give an alternative, simpler algorithm to extract a single such pair.This combinatorial theorem then comes handy in rounding a fractional solution of an LP relaxation of the maximum Traveling Salesman Problem (TSP) problem. The first stage of the rounding procedure obtains two cycle covers that do not share a 2-cycle with weight at least twice the weight of the optimal solution. Then we show how to extract a tour from the 2 cycle covers, whose weight is at least 2/3 of the weight of the longest tour. This improves upon the previous 5/8 approximation with a simpler algorithm. Utilizing a reduction from maximum TSP to the shortest superstring problem, we obtain a 2.5-approximation algorithm for the latter problem, which is again much simpler than the previous one.For minimum asymmetric TSP, the same technique gives two cycle covers, not sharing a 2-cycle, with weight at most twice the weight of the optimum. Assuming triangle inequality, we then show how to obtain from this pair of cycle covers a tour whose weight is at most 0.842 log2 n larger than optimal. This improves upon a previous approximation algorithm with approximation guarantee of 0.999 log2 n. Other applications of the rounding procedure are approximation algorithms for maximum 3-cycle cover (factor 2/3, previously 3/5) and maximum asymmetric TSP with triangle inequality (factor 10/13, previously 3/4).