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Competitive Online Approximation of the Optimal Search Ratio

Rudolf Fleischer, Tom Kamphans, Rolf Klein, Elmar Langetepe, Gerhard Trippen
2008 SIAM journal on computing (Print)  
We answer these questions for simple polygons and for undirected graphs, by providing online search strategies that are as good as the best offline search algorithms, up to a constant factor.  ...  How efficiently can we search an unknown environment for a goal in unknown position? How much would it help if the environment were known?  ...  For an approximation of the optimal search ratio, we compare the online path to the best possible offline path, which-in turn-may already have a bad competitive ratio.  ... 
doi:10.1137/060662204 fatcat:46hnlkwgzne3lc4ertgvipx6ji

Competitive Online Approximation of the Optimal Search Ratio [chapter]

Rudolf Fleischer, Tom Kamphans, Rolf Klein, Elmar Langetepe, Gerhard Trippen
2004 Lecture Notes in Computer Science  
We answer these questions for simple polygons and for undirected graphs, by providing online search strategies that are as good as the best offline search algorithms, up to a constant factor.  ...  How efficiently can we search an unknown environment for a goal in unknown position? How much would it help if the environment were known?  ...  For an approximation of the optimal search ratio, we compare the online path to the best possible offline path, which-in turn-may already have a bad competitive ratio.  ... 
doi:10.1007/978-3-540-30140-0_31 fatcat:hmcx46y6qrhlbisxmgahbbv25u

On Revenue Maximization in Second-Price Ad Auctions [chapter]

Yossi Azar, Benjamin Birnbaum, Anna R. Karlin, C. Thach Nguyen
2009 Lecture Notes in Computer Science  
and randomized online algorithms achieving better competitive ratios.  ...  On the positive side, we provide a 2-approximation for offline 2PM and a 5.083-competitive randomized algorithm for online 2PM.  ...  [10] present an algorithm for the online version that achieves an optimal competitive ratio of e/(e − 1) for the case when the bids are much smaller than the budgets, a result also proved by Buchbinder  ... 
doi:10.1007/978-3-642-04128-0_14 fatcat:5wkfhhnu7jexrhd3amuo4ym7ra

Page 6953 of Mathematical Reviews Vol. , Issue 2002I [page]

2002 Mathematical Reviews  
When D approaches infinity, this provides an optimal online strategy for the unbounded case with competitive ratio 9.  ...  A basic idea of the approach is to solve the dual question: Given a competitive ratio r, what is the largest extent that can be searched without violating r?  ... 

Combinatorial Online Optimization in Real Time [chapter]

Martin Grötschel, Sven O. Krumke, Jörg Rambau, Thomas Winter, Uwe T. Zimmermann
2001 Online Optimization of Large Scale Systems  
Optimization is the task of finding an optimum solution to a given problem. When the decision variables are discrete we speak of a combinatorial optimization problem.  ...  This paper surveys the are of combinatorial online and real-time optimization, it discusses, in particular, the concepts with which online and real-time algorithms can be analyzed.  ...  Approximation algorithms for offline minimization problems are closely related to competitive online algorithms. By the above definition, a c-competitive online algorithm is c-approximative.  ... 
doi:10.1007/978-3-662-04331-8_33 fatcat:sbn7zuddmfbphmeq6dbrvasvom

On-line network optimization problems [chapter]

Bala Kalyanasundaram, Kirk Pruhs
1998 Lecture Notes in Computer Science  
We survey results on online versions of the standard network optimization problems, including the minimum spanning tree problem, the minimum Steiner tree problem, the weighted and unweighted matching problems  ...  The goal in these problems is to maintain, with minimal changes, a low cost subgraph of some type in a dynamically changing network.  ...  Open Question: What is the optimal competitive ratio in terms of m, the number of sites, for the online transportation problem? It seems that there should be an 2m ? 1 competitive algorithm.  ... 
doi:10.1007/bfb0029573 fatcat:kdh23xb4mnbelhcim36r6httea

SIGACT news online algorithms column 10

Marek Chrobak, Claire Kenyon-Mathieu
2006 ACM SIGACT News  
The worst case in (1) is when u = d k−1 , and routine calculations show that this strategy's competitive ratio is 4, which also turns out to be optimal in the deterministic setting.  ...  Express the ratio (1) as the product of ( ≤k d )/d k by d k /u.  ...  online bidding ratio (1), so the deterministic competitive ratio is bounded by 4 and the randomized competitive ratio is bounded by e.  ... 
doi:10.1145/1189056.1189078 fatcat:l4dmwjvs6jes7lscn664qcw3s4

SIGACT news online algorithms column 2

Marek Chrobak
2004 ACM SIGACT News  
The worst case in (1) is when u = d k−1 , and routine calculations show that this strategy's competitive ratio is 4, which also turns out to be optimal in the deterministic setting.  ...  Express the ratio (1) as the product of ( ≤k d )/d k by d k /u.  ...  online bidding ratio (1), so the deterministic competitive ratio is bounded by 4 and the randomized competitive ratio is bounded by e.  ... 
doi:10.1145/970831.970841 fatcat:aouhalb5yvacjdspnm4hpucifu

Competitive solutions for online financial problems

Ran El-Yaniv
1998 ACM Computing Surveys  
This article surveys results concerning online algorithms for solving problems related to the management of money and other assets.  ...  In particular, the survey focuses on search, replacement, and portfolio selection problems.  ...  I also thank Susanne Albers, Robert Aumann, Dean Online Financial Problems •  ... 
doi:10.1145/274440.274442 fatcat:qdturxrdhrd3tmoybf6jaszln4

Competitive solutions for on-line financial problems [chapter]

Ran El-Yaniv
1998 Lecture Notes in Computer Science  
This article surveys results concerning online algorithms for solving problems related to the management of money and other assets.  ...  In particular, the survey focuses on search, replacement, and portfolio selection problems.  ...  I also thank Susanne Albers, Robert Aumann, Dean Online Financial Problems •  ... 
doi:10.1007/bfb0029576 fatcat:5k7rjsypyrdzhkrfsxxdb2gai4

Online Multi-path Routing in a Maze [chapter]

Stefan Rührup, Christian Schindelhauer
2006 Lecture Notes in Computer Science  
It is known that a flooding strategy like expanding ring search can route a message linear in the minimum number of steps d while it causes a traffic (i.e. the total number of messages) of O(d 2 ).  ...  For optimizing traffic a single-path strategy is optimal producing traffic O(d+p), where p is the number of nodes that are adjacent to faulty nodes.  ...  Comparing the time of the algorithm with the optimal time leads to the competitive ratio, which is well known in the field of online algorithms [4] . Definition 1.  ... 
doi:10.1007/11940128_65 fatcat:73c4lxhf65htlb2u7k56xq2vtq

Online Financial Algorithms: Competitive Analysis

Sandeep Kumar, Deepak Garg
2012 International Journal of Computer Applications  
Among these, an online financial algorithm is one of the most important areas where lots of efforts have been used to produce an efficient algorithm.  ...  Online Algorithms have found their applicability in broad areas of computer engineering.  ...  A simple randomized search algorithm can attain a competitive ratio of O(log φ) [3] .In order to obtain an optimal competitive ratio it requires a more involved strategy.  ... 
doi:10.5120/4974-7228 fatcat:5s734zztwre37k5q3zl25lmzie

Allocating online advertisement space with unreliable estimates

Mohammad Mahdian, Hamid Nazerzadeh, Amin Saberi
2007 Proceedings of the 8th ACM conference on Electronic commerce - EC '07  
We study the problem of optimally allocating online advertisement space to budget-constrained advertisers.  ...  This problem was defined and studied from the perspective of worst-case online competitive analysis by Mehta et al.  ...  The last two authors are supported by NSF award 0546889 and a gift from Google.  ... 
doi:10.1145/1250910.1250952 dblp:conf/sigecom/MahdianNS07 fatcat:z32esndp5zaoveo5beftqccwsm

Optimal Analysis of an Online Algorithm for the Bipartite Matching Problem on a Line

Sharath Raghvendra, Marc Herbstritt
2018 International Symposium on Computational Geometry  
The well-known Work Function Algorithm (WFA) has a competitive ratio of O(n) and Ω(log n) for this problem.  ...  In the online metric bipartite matching problem, we are given a set S of server locations in a metric space.  ...  For the k-server problem, the competitive ratio of the WFA is 2k − 1 [6] which is near optimal with a lower bound of k on the competitive ratio of any algorithm in any metric space that has at least k  ... 
doi:10.4230/lipics.socg.2018.67 dblp:conf/compgeom/Raghvendra18 fatcat:gmf4lsrylbhs7pchk665252xde

Budget Constrained Bidding in Keyword Auctions and Online Knapsack Problems [chapter]

Yunhong Zhou, Deeparnab Chakrabarty, Rajan Lukose
2008 Lecture Notes in Computer Science  
We design both deterministic and randomized algorithms for the online (multiple-choice) knapsack problems achieving a provably optimal competitive ratio.  ...  We consider the budget-constrained bidding optimization problem for sponsored search auctions, and model it as an online (multiple-choice) knapsack problem.  ...  In general, no online algorithm can achieve any non-trivial competitive ratio (the ratio between the output of the given algorithm and the offline optimum) for Online-KP [4] .  ... 
doi:10.1007/978-3-540-92185-1_63 fatcat:ykx7fgdus5aode6dvaaltznxgy
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