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Competitive Online Approximation of the Optimal Search Ratio

2008
*
SIAM journal on computing (Print)
*

We answer these questions for simple polygons and for undirected graphs, by providing

doi:10.1137/060662204
fatcat:46hnlkwgzne3lc4ertgvipx6ji
*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*. ...##
###
Competitive Online Approximation of the Optimal Search Ratio
[chapter]

2004
*
Lecture Notes in Computer Science
*

We answer these questions for simple polygons and for undirected graphs, by providing

doi:10.1007/978-3-540-30140-0_31
fatcat:hmcx46y6qrhlbisxmgahbbv25u
*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*. ...##
###
On Revenue Maximization in Second-Price Ad Auctions
[chapter]

2009
*
Lecture Notes in Computer Science
*

and randomized

doi:10.1007/978-3-642-04128-0_14
fatcat:5wkfhhnu7jexrhd3amuo4ym7ra
*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 ...##
###
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]

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*. ...

##
###
On-line network optimization problems
[chapter]

1998
*
Lecture Notes in Computer Science
*

We survey results on

doi:10.1007/bfb0029573
fatcat:kdh23xb4mnbelhcim36r6httea
*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. ...##
###
SIGACT news online algorithms column 10

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. ...

##
###
SIGACT news online algorithms column 2

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. ...

##
###
Competitive solutions for online financial problems

1998
*
ACM Computing Surveys
*

This article surveys results concerning

doi:10.1145/274440.274442
fatcat:qdturxrdhrd3tmoybf6jaszln4
*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 • ...##
###
Competitive solutions for on-line financial problems
[chapter]

1998
*
Lecture Notes in Computer Science
*

This article surveys results concerning

doi:10.1007/bfb0029576
fatcat:5k7rjsypyrdzhkrfsxxdb2gai4
*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 • ...##
###
Online Multi-path Routing in a Maze
[chapter]

2006
*
Lecture Notes in Computer Science
*

It is known that a flooding strategy like expanding ring

doi:10.1007/11940128_65
fatcat:73c4lxhf65htlb2u7k56xq2vtq
*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. ...##
###
Online Financial Algorithms: Competitive Analysis

2012
*
International Journal of Computer Applications
*

Among these, an

doi:10.5120/4974-7228
fatcat:5s734zztwre37k5q3zl25lmzie
*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. ...##
###
Allocating online advertisement space with unreliable estimates

2007
*
Proceedings of the 8th ACM conference on Electronic commerce - EC '07
*

We study

doi:10.1145/1250910.1250952
dblp:conf/sigecom/MahdianNS07
fatcat:z32esndp5zaoveo5beftqccwsm
*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. ...##
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Optimal Analysis of an Online Algorithm for the Bipartite Matching Problem on a Line

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 ...

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

2008
*
Lecture Notes in Computer Science
*

We design both deterministic and randomized algorithms for

doi:10.1007/978-3-540-92185-1_63
fatcat:ykx7fgdus5aode6dvaaltznxgy
*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] . ...
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