TY - GEN A1 - Krumke, Sven T1 - News from the Online Traveling Repairman N2 - The traveling repairman problem (TRP) is a variant of the famous traveling salesman problem (TSP). The objective for the TRP is to minimize the latency, that is the the weighted sum of completion times of the cities, where the completion time of a city is defined to be the time in the tour before the city is reached. In the online traveling repairman problem (OLTRP) requests for visits to cities (points in a metric space) arrive online while the repairman is traveling. We analyze the performance of algorithms using competitive analysis, where the cost of an online algorithm is compared to that of an optimal offline algorithm. An optimal offline algorithm knows the entire request sequence in advance and can serve it with minimum cost. Recently, Feuerstein and Stougie presented a $9$-competitive algorithm for the OLTRP on the real line. In this paper we show how to use techniques from online-scheduling to obtain an $8$-competitive deterministic algorithm which works for any metric space. We also present a randomized algorithm which has a competitive ratio of $\frac{4}{\ln 2}\approx 5.7708$ against an oblivious adversary. All of our results also hold for the ``dial-a-ride'' generalization of the OLTRP, where objects have to be picked up and delivered by a server. T3 - ZIB-Report - 00-08 KW - Traveling Repairman KW - Latency KW - Dial-a-Ride-Problem KW - Competitive Analysis Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-5767 ER - TY - GEN A1 - Blom, Michiel A1 - Krumke, Sven A1 - Paepe, Willem de A1 - Stougie, Leen T1 - The Online-TSP Against Fair Adversaries N2 - In the online traveling salesman problem requests for visits to cities (points in a metric space) arrive online while the salesman is traveling. The salesman moves at no more than unit speed and starts and ends his work at a designated origin. The objective is to find a routing for the salesman which finishes as early as possible. Performance of algorithms is measured through their competitive ratio, comparing the outcome of the algorithms with that of an adversary who provides the problem instance and therefore is able to achieve the optimal offline solution. Objections against such omnipotent adversaries have lead us to devise an adversary that is in a natural way, in the context of routing problems, more restricted in power. For the exposition we consider the online traveling salesman problem on the metric space given by the non-negative part of the real line. We show that a very natural strategy is~$3/2$-competitive against the conventional adversary, which matches the lower bound on competitive ratios achievable for algorithms for this problem. Against the more ``\emph{fair adversary}'', that we propose, we show that there exists an algorithm with competitive ratio $\frac{1+\sqrt{17}}{4}\approx 1.28$ and provide a matching lower bound. We also show competitiveness results for a special class of algorithms (called zealous algorithms) that do not allow waiting time for the server as long as there are requests unserved. T3 - ZIB-Report - 00-09 KW - Vehicle Routing KW - Online-Algorithms KW - Competitive Analysis Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-5779 ER -