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Online Routing Problems: Value of Advanced Information as Improved Competitive Ratios
, 2006
"... We consider online versions of the traveling salesman problem (TSP) and traveling repairman problem (TRP) where instances are not known in advance. Cities (points) to be visited are revealed over time, while the server is enroute serving previously released requests. These problems are known in the ..."
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Cited by 16 (3 self)
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We consider online versions of the traveling salesman problem (TSP) and traveling repairman problem (TRP) where instances are not known in advance. Cities (points) to be visited are revealed over time, while the server is enroute serving previously released requests. These problems are known in the literature as the online TSP (TRP, respectively). The corresponding offline problems are the TSP (TRP) with release dates, problems where each point has to be visited at or after a given release date. In the current literature, the assumption is that a request becomes known at the time of its release date. In this paper we introduce the notion of a request’s disclosure date, the time whena city’s locatio nand release date are revealed to the server. In a variety of disclosure date scenarios and metric spaces, we give new online algorithms and quantify the value of this advanced information in the form of improved competitive ratios. We also provide a general result on polynomialtime online algorithms for the online TSP.
Algorithms for the online quota traveling salesman problem
 Information Processing Letters
, 2004
"... Abstract. The Quota Traveling Salesman Problem is a generalization of the well known Traveling Salesman Problem. The goal of the traveling salesman is, in this case, to reach a given quota of the sales, minimizing the amount of time. In this paper we address the online version of the problem, where ..."
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Cited by 11 (3 self)
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Abstract. The Quota Traveling Salesman Problem is a generalization of the well known Traveling Salesman Problem. The goal of the traveling salesman is, in this case, to reach a given quota of the sales, minimizing the amount of time. In this paper we address the online version of the problem, where requests are given over time. We present algorithms for various metric spaces, and analyze their performance in the usual framework of the competitive analysis. In particular we present a 2competitive algorithm that matches the lower bound for general metric spaces. In the case of the halfline metric space, we show that it is helpful not to move at full speed, and this approach is also used to derive the best online polynomial time algorithm known so far for the more general OnLine TSP problem (in the homing version). 1
The online asymmetric traveling salesman problem
 Proc. 9th Workshop on Algorithms and Data Structures, volume 3608 of Lecture Notes in Computer Science
, 2005
"... Abstract. We consider two online versions of the asymmetric traveling salesman problem with triangle inequality. For the homing version, in which the salesman is required to return in the city where it started from, we give a 3+√5competitive algorithm and prove that this is best 2 possible. For th ..."
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Cited by 7 (4 self)
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Abstract. We consider two online versions of the asymmetric traveling salesman problem with triangle inequality. For the homing version, in which the salesman is required to return in the city where it started from, we give a 3+√5competitive algorithm and prove that this is best 2 possible. For the nomadic version, the online analogue of the shortest asymmetric hamiltonian path problem, we show that the competitive ratio of any online algorithm depends on the amount of asymmetry of the space in which the salesman moves. We also give bounds on the competitive ratio of online algorithms that are zealous, that is, in which the salesman cannot stay idle when some city can be served. 1
Discrete Online And RealTime Optimization
 Proceedings of the 15th IFIP World Computer Congress, Budapest/Vienna
, 1998
"... Discrete Optimization techniques have become a major and successful tool for modelling and solving many real world problems. In modelling realtime applications, we often have to face the inherent difficulty that an essential part of the data arrives sequentially in realtime, and that decision supp ..."
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Cited by 4 (4 self)
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Discrete Optimization techniques have become a major and successful tool for modelling and solving many real world problems. In modelling realtime applications, we often have to face the inherent difficulty that an essential part of the data arrives sequentially in realtime, and that decision support is requested at the same time. Online and realtime algorithms are designed to handle such difficulties. We review some theoretical and practical aspects of online algorithms. Starting with theoretical concepts for performance evaluation, we survey typical results for classical optimization problems of discrete structure. Finally, we describe results on solving Discrete Optimization models for some realtime applications. Discrete Optimization has become a major and successful tool in modelling and solving real world problems arising in computer science, in economics, and in engineering. This success is based on two essential facts: computation times have decreased dramatically by the im...
Online kserver routing problems
 Proceedings of the 4th Workshop on on Approximation and Online Algorithms, Lecture Notes in Computer Science
, 2006
"... In an online kserver routing problem, a crew of k servers has to visit points in a metric space as they arrive in real time. Possible objective functions include minimizing the makespan (kTraveling Salesman Problem) and minimizing the average completion time (kTraveling Repairman Problem). We g ..."
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Cited by 3 (1 self)
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In an online kserver routing problem, a crew of k servers has to visit points in a metric space as they arrive in real time. Possible objective functions include minimizing the makespan (kTraveling Salesman Problem) and minimizing the average completion time (kTraveling Repairman Problem). We give competitive algorithms, resource augmentation results and lower bounds for kserver routing problems on several classes of metric spaces. Surprisingly, in some cases the competitive ratio is dramatically better than that of the corresponding single server problem. Namely, we give a 1 + O(log k/k)competitive algorithm for the kTraveling Salesman Problem and the kTraveling Repairman Problem when the underlying metric space is the real line. We also prove that similar results cannot hold for the Euclidean plane.
Online Graph Exploration: New Results on Old and New Algorithms
"... Abstract. We study the problem of exploring an unknown undirected connected graph. Beginning in some start vertex, a searcher must visit each node of the graph by traversing edges. Upon visiting a vertex for the first time, the searcher learns all incident edges and their respective traversal costs. ..."
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Cited by 3 (1 self)
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Abstract. We study the problem of exploring an unknown undirected connected graph. Beginning in some start vertex, a searcher must visit each node of the graph by traversing edges. Upon visiting a vertex for the first time, the searcher learns all incident edges and their respective traversal costs. The goal is to find a tour of minimum total cost. Kalyanasundaram and Pruhs [23] proposed a sophisticated generalization of a Depth First Search that is 16competitive on planar graphs. While the algorithm is feasible on arbitrary graphs, the question whether it has constant competitive ratio in general has remained open. Our main result is an involved lower bound construction that answers this question negatively. On the positive side, we prove that the algorithm has constant competitive ratio on any class of graphs with bounded genus. Furthermore, we provide a constant competitive algorithm for general graphs with a bounded number of distinct weights. 1
On minimizing the maximum flow time in the online dialaride problem
, 2005
"... In the online dialaride problem (OlDarp), objects must be transported by a server between points in a metric space. Transportation requests (“rides”) arrive online, specifying the objects to be transported and the corresponding source and destination. We investigate the OlDarp for the objective ..."
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Cited by 1 (1 self)
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In the online dialaride problem (OlDarp), objects must be transported by a server between points in a metric space. Transportation requests (“rides”) arrive online, specifying the objects to be transported and the corresponding source and destination. We investigate the OlDarp for the objective of minimizing the maximum flow time. It has been well known that there can be no strictly competitive online algorithm for this objective and no competitive algorithm at all on unbounded metric spaces. However, the question whether on metric spaces with bounded diameter there are competitive algorithms if one allows an additive constant in the definition competitive ratio, had been open for quite a while. We provide a negative answer to this question already on the uniform metric space with three points. Our negative result is complemented by a strictly 2competitive algorithm for the Online Traveling Salesman Problem on the uniform metric space, a special case of the problem.
Benchmarking Algorithms for Dynamic Travelling Salesman Problems
"... Abstract Dynamic optimisation problems are becoming increasingly important; meanwhile, progress in optimisation techniques and in computational resources are permitting the development of effective systems for dynamic optimisation, resulting in a need for objective methods to evaluate and compare d ..."
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Cited by 1 (0 self)
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Abstract Dynamic optimisation problems are becoming increasingly important; meanwhile, progress in optimisation techniques and in computational resources are permitting the development of effective systems for dynamic optimisation, resulting in a need for objective methods to evaluate and compare different techniques. The search for effective techniques may be seen as a multiobjective problem, trading off time complexity against effectiveness; hence benchmarks must be able to compare techniques across the Pareto front, not merely at a single point. We propose benchmarks for the Dynamic Travelling Salesman Problem, adapted from the CHN144 benchmark of 144 Chinese cities for the static Travelling Salesman Problem. We provide an example of the use of the benchmark, and illustrate the information that can be gleaned from analysis of the algorithm performance on the benchmarks. I.
New Competitive Ratios for Generalized Online Routing
, 2006
"... We consider online routing optimization problems where the objective is to minimize the time needed to visit a set of locations under various constraints; the problems are online because the set of locations are revealed incrementally over time. We make no probabilistic assumptions whatsoever about ..."
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We consider online routing optimization problems where the objective is to minimize the time needed to visit a set of locations under various constraints; the problems are online because the set of locations are revealed incrementally over time. We make no probabilistic assumptions whatsoever about the problem data. We consider two main problems: (1) the online Traveling Salesman Problem (TSP) with precedence and capacity constraints and (2) the online TSP with m salesmen. For both problems we propose online algorithms, each with a competitive ratio of 2; for the msalesmen problem, we show our result is bestpossible. We also consider polynomialtime online algorithms as well as various generalizations of our results. 1