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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 19 (4 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 12 (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
Nonabusiveness helps: an O(1)competitive algorithm for minimizing the maximum flow time in the online traveling salesman problem
 Proc. 5th Int. Workshop on Approximation Algorithms for Combinatorial Optimization
, 2002
"... Abstract. In the online traveling salesman problem (OlTsp) requests for visits to cities arrive online while the salesman is traveling. We study the FmaxOlTsp where the objective is to minimize the maximum flow time. This objective is particularly interesting for applications. Unfortunately, there ..."
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Abstract. In the online traveling salesman problem (OlTsp) requests for visits to cities arrive online while the salesman is traveling. We study the FmaxOlTsp where the objective is to minimize the maximum flow time. This objective is particularly interesting for applications. Unfortunately, there can be no competitive algorithm, neither deterministic nor randomized. Hence, competitive analysis fails to distinguish online algorithms. Not even resource augmentation which is helpful in scheduling works as a remedy. This unsatisfactory situation motivates the search for alternative analysis methods. We introduce a natural restriction on the adversary for the FmaxOlTsp on the real line. A nonabusive adversary may only move in a direction if there are yet unserved requests on this side. Our main result is an algorithm which achieves a constant competitive ratio against the nonabusive adversary. 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 9 (5 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
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 9 (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
Discrete online and realtime optimization
 Proceedings of the 15th IFIP World Computer Congress, Budapest/Vienna
, 1998
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Online multiserver dialaride problems
, 2006
"... Abstract. In an online dialaride problem, a crew of servers has to process transportation requests as they arrive in real time. Possible objective functions include minimizing the makespan and minimizing the sum of completion times. We give competitive algorithms and negative results for several ..."
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Cited by 3 (1 self)
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Abstract. In an online dialaride problem, a crew of servers has to process transportation requests as they arrive in real time. Possible objective functions include minimizing the makespan and minimizing the sum of completion times. We give competitive algorithms and negative results for several online dialaride problems with multiple servers. Surprisingly, in some cases the competitive ratio is dramatically better than that of the corresponding single server problem. 1
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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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.