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16
Algorithms for the Online Travelling Salesman
 ALGORITHMICA
, 2001
"... In this paper the problem of efficiently serving a sequence of requests presented in an online fashion located at points of a metric space is considered. We call this problem the OnLine Travelling Salesman Problem (OLTSP). It has a variety of relevant applications in logistics and robotics. We ..."
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Cited by 24 (7 self)
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In this paper the problem of efficiently serving a sequence of requests presented in an online fashion located at points of a metric space is considered. We call this problem the OnLine Travelling Salesman Problem (OLTSP). It has a variety of relevant applications in logistics and robotics. We consider two
Reordering Buffers for General Metric Spaces
, 2007
"... In the reordering buffer problem, we are given an input sequence of requests for service each of which corresponds to a point in a metric space. The cost of serving the requests heavily depends on the processing order. Serving a request induces cost corresponding to the distance between itself and t ..."
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Cited by 7 (2 self)
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In the reordering buffer problem, we are given an input sequence of requests for service each of which corresponds to a point in a metric space. The cost of serving the requests heavily depends on the processing order. Serving a request induces cost corresponding to the distance between itself and the previously served request, measured in the underlying metric space. A reordering buffer with storage capacity k can be used to reorder the input sequence in a restricted fashion so as to construct an output sequence with lower service cost. This simple and universal framework is useful for many applications in computer science and economics, e. g., disk scheduling, rendering in computer graphics, or painting shops in car plants. In this paper, we design online algorithms for the reordering buffer problem. Our main result is a strategy with a polylogarithmic competitive ratio for general metric spaces. Previous work on the reordering buffer problem only considered very restricted metric spaces. We obtain our result by first developing a deterministic algorithm for arbitrary weighted trees with a competitive ratio of O(D · log k), where D denotes the unweighted diameter of the tree, i. e., the maximum number of edges on a path connecting two nodes. Then we show how to improve this competitive ratio to O(log 2 k) for metric spaces that are derived from HSTs. Combining this result with the results on probabilistically approximating arbitrary metrics by tree metrics, we obtain a randomized strategy for general metric spaces that achieves a competitive ratio of O(log 2 k · log n) in expectation against an oblivious adversary. Here n denotes the number of distinct points in the metric space. Note that the length of the input sequence can be much larger than n.
The power of reordering for online minimum makespan scheduling
 In Proc. 49th FOCS
"... In the classic minimum makespan scheduling problem, we are given an input sequence of jobs with processing times. A scheduling algorithm has to assign the jobs to m parallel machines. The objective is to minimize the makespan, which is the time it takes until all jobs are processed. In this paper, w ..."
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Cited by 7 (1 self)
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In the classic minimum makespan scheduling problem, we are given an input sequence of jobs with processing times. A scheduling algorithm has to assign the jobs to m parallel machines. The objective is to minimize the makespan, which is the time it takes until all jobs are processed. In this paper, we consider online scheduling algorithms without preemption. However, we do not require that each arriving job has to be assigned immediately to one of the machines. A reordering buffer with limited storage capacity can be used to reorder the input sequence in a restricted fashion so as to schedule the jobs with a smaller makespan. This is a natural extension of lookahead. We present an extensive study of the power and limits of online reordering for minimum makespan scheduling. As main result, we give, for m identical machines, tight and, in comparison to the problem without reordering, much improved bounds on the competitive ratio for minimum makespan scheduling with reordering buffers. Depending on m, the achieved competitive ratio lies between 4/3 and 1.4659. This optimal ratio is achieved with a buffer of size Θ(m). We show that larger buffer sizes do not result in an additional advantage and that a buffer of size Ω(m) is necessary to achieve this competitive ratio. Further, we present several algorithms for different buffer sizes. Among others, we introduce, for every buffer size k ∈ [1,(m + 1)/2], a (2 − 1/(m − k + 1))competitive algorithm, which nicely generalizes the wellknown result of Graham. For m uniformly related machines, we give a scheduling algorithm that achieves a competitive ratio of 2 with a reordering buffer of size m. Considering that the best known ∗ Supported by DFG grant WE 2842/1. competitive ratio for uniformly related machines without reordering is 5.828, this result emphasizes the power of online reordering further more. 1.
Web Caching with Request Reordering
, 2002
"... Current web caching algorithms process requests in the order of the arrival. While such restriction is inevitable in system paging due to the sequential nature of a program, the HTTP requests are (essentially) independent at a high volume proxy server. This gives a proxy server the exibility to reor ..."
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Cited by 6 (0 self)
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Current web caching algorithms process requests in the order of the arrival. While such restriction is inevitable in system paging due to the sequential nature of a program, the HTTP requests are (essentially) independent at a high volume proxy server. This gives a proxy server the exibility to reorder requests, provided no request is inordinately delayed. The expectation is that reordering requests may lead to better performance. We formulate an online k reordering problem that captures such phenomenon for unit caches. We give a dynamic programming algorithm to solve the oine case. We give O(1) upper and lower bound on the competitive ratio of the online algorithms. We also generalize this problem to any metric space.
Surviving ObjectOriented Projects
, 2004
"... CWI is a founding member of ERCIM, the European Research Consortium for Informatics and Mathematics. CWI's research has a themeoriented structure and is grouped into four clusters. Listed below are the names of the clusters and in parentheses their acronyms. ..."
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Cited by 5 (0 self)
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CWI is a founding member of ERCIM, the European Research Consortium for Informatics and Mathematics. CWI's research has a themeoriented structure and is grouped into four clusters. Listed below are the names of the clusters and in parentheses their acronyms.
OnLine MultiThreaded Scheduling
, 1999
"... This paper presents results on online scheduling problems with multiple threads. The jobs are organized in a number of sequences called threads. Each job becomes available (is presented) only at the moment a scheduling decision is made on all the preceding jobs in the same thread. Thus, apart from ..."
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Cited by 2 (1 self)
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This paper presents results on online scheduling problems with multiple threads. The jobs are organized in a number of sequences called threads. Each job becomes available (is presented) only at the moment a scheduling decision is made on all the preceding jobs in the same thread. Thus, apart from decisions on scheduling of jobs also decisions are required on the order of exploring the threads. We consider two different online paradigms. The first paradigm can be regarded as constructing, in an online way, a schedule of the jobs which is to be executed later, a sort of batch process. The other paradigm models a realtime planning situation, in which the jobs are immediately executed at the moment they are assigned to a machine. We study two classical objective functions: the makespan dened as the maximum completion time of the jobs, and the average completion time of the jobs, also called the latency. We establish a fairly complete set of results for these online multithreaded ...
Competitive Caching of Query Results in Search Engines Abstract
"... We study the problem of caching query result pages in Web search engines. Popular search engines receive millions of queries per day, and for each query, return a result page to the user who submitted the query. The user may request additional result pages for the same query, submit a new query, or ..."
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Cited by 2 (1 self)
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We study the problem of caching query result pages in Web search engines. Popular search engines receive millions of queries per day, and for each query, return a result page to the user who submitted the query. The user may request additional result pages for the same query, submit a new query, or quit searching altogether. An efficient scheme for caching query result pages may enable search engines to lower their response time and reduce their hardware requirements. This work studies query result caching within the framework of the competitive analysis of algorithms. We define a discrete time stochastic model for the manner in which queries are submitted to search engines by multiple user sessions. We then present an adaptation of a known online paging scheme to this model. The expected number of cache misses of the resulting algorithm is no greater than 4 times the expected number of misses that any online caching algorithm will experience under our specific model of query generation. 1
Different Competitiveness Measures for Infinite Multithreaded Paging
, 1998
"... The Multithreaded Paging problem (MTP) generalizes Paging to the case where there are many threads of requests. This models situations in which the requests come from more than one independent source. At each step it is necessary to decide which request to serve, and also (as in normal Paging) whic ..."
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Cited by 1 (1 self)
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The Multithreaded Paging problem (MTP) generalizes Paging to the case where there are many threads of requests. This models situations in which the requests come from more than one independent source. At each step it is necessary to decide which request to serve, and also (as in normal Paging) which page of fast memory to remove on a page fault. In MTP the input sequences are allowed to be either finite or infinite, and the problem is considered both with and without a fairness constraint on the way in which the individual requests are served. In this paper we propose alternative definitions of competitiveness for deterministic online algorithms for the infinite versions of MTP. The new definitions intend to compare the algorithms' steadystate performances on infinite sequences. Although a priori the alternative definitions seem different, we find that they are essentially equivalent. This suggests that the somehow negative results obtained when MTP was introduced, may be consider...
An Improved Competitive Algorithm for Reordering Buffer Management §
"... log k log log k We design and analyze an online reordering buffer) management algorithm with improved O competitive ratio for nonuniform costs, where k is the buffer size. This improves on the best previous result (even for uniform costs) of Englert and Westermann (ICALP 2005) giving O(log k) comp ..."
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Cited by 1 (0 self)
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log k log log k We design and analyze an online reordering buffer) management algorithm with improved O competitive ratio for nonuniform costs, where k is the buffer size. This improves on the best previous result (even for uniform costs) of Englert and Westermann (ICALP 2005) giving O(log k) competitive ratio, which was also the best (offline) polynomial time approximation guarantee for this problem. Our analysis is based on an intricate dual fitting argument using a linear programming relaxation for the problem that we introduce in this paper. 1