STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
When Trees Collide: An Approximation Algorithm for theGeneralized Steiner Problem on Networks
SIAM Journal on Computing
A General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
A constant-factor approximation algorithm for the k MST problem (extended abstract)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
A 2.5-factor approximation algorithm for the k-MST problem
Information Processing Letters
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
Approximation schemes for minimum latency problems
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
An improved approximation ratio for the minimum latency problem
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
A 3-approximation for the minimum tree spanning k vertices
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
The Minimum Latency Problem Is NP-Hard for Weighted Trees
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
Improved approximation algorithms for the minimum latency problem via prize-collecting strolls
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume Part I
Physical search problems with probabilistic knowledge
Artificial Intelligence
Expert Systems with Applications: An International Journal
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The Traveling Salesman Problem (TSP) is a classical problem in discrete optimization. Its paradigmatic character makes it one of the most studied in computer science and operations research and one for which an impressive amount of algorithms (in particular heuristics and approximation algorithms) have been proposed. While in the general case the problem is known not to allow any constant ratio approximation algorithm and in the metric case no better algorithm than Christofides' algorithm is known, which guarantees an approximation ratio of 3/2, recently an important breakthrough by Arora has led to the definition of a new polynomial approximation scheme for the Euclidean case. A growing attention has also recently been posed on the approximation of other paradigmatic routing problems such as the Travelling Repairman Problem (TRP). The altruistic Travelling Repairman seeks to minimimize the average time incurred by the customers to be served rather than to minimize its working time like the egoistic Travelling Salesman does. The new approximation scheme for the Travelling Salesman is also at the basis of a new approximation scheme for the Travelling Repairman problem in the euclidean space. New interesting constant approximation algorithms have recently been presented also for the Travelling Repairman on general metric spaces. Interesting applications of this line of research can be found in the problem of routing agents over the web. In fact the problem of programming a "spider" for efficiently searching and reporting information is a clear example of potential applications of algorithms for the above mentioned problems. These problems are very close in spirit to the problem of searching an object in a known graph introduced by Koutsoupias, Papadimitriou and Yannakakis [14]. In this paper, motivated by web searching applications, we summarize the most important recent results concerning the approximate solution of the TRP and the TSP and their application and extension to web searching problems.