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Approximating Min-Max (Regret) Versions of Some Polynomial Problems [chapter]

Hassene Aissi, Cristina Bazgan, Daniel Vanderpooten
2006 Lecture Notes in Computer Science  
Applying this scheme to shortest path and minimum spanning tree, we obtain fully polynomial-time approximation schemes with much better running times than the ones previously presented in the literature  ...  For a bounded number of scenarios, we establish a general approximation scheme which can be used for min-max and min-max regret versions of some polynomial problems.  ...  An optimization problem has a fully polynomial-time approximation scheme (an fptas, for short) if, for every constant ε > 0, it admits an (1 + ε)-approximation algorithm which is polynomial both in the  ... 
doi:10.1007/11809678_45 fatcat:xhxydjkcibdajbl2z6tnzdptle

An FPTAS for the Knapsack Problem with Parametric Weights [article]

Michael Holzhauser, Sven O. Krumke
2017 arXiv   pre-print
We present the first fully polynomial-time approximation scheme (FPTAS) for the problem that, for any desired precision ε∈ (0,1), computes (1-ε)-approximate solutions for all values of the parameter.  ...  ,n}}} for a knapsack with capacity W.  ...  In this paper, we are interested in a fully polynomial time approximation scheme for the parametric weight knapsack problem.  ... 
arXiv:1703.06048v1 fatcat:nyosa2im6vfwve2276nlyqicc4

Combinatorial Approximation Algorithms for Generalized Flow Problems

Jeffrey D Oldham
2001 Journal of Algorithms  
Using this generalized shortest paths algorithm, we present fully polynomial-time approximation schemes for the generalized versions of the maximum flow, the nonnegative-cost minimum-cost flow, the concurrent  ...  We present a strongly polynomial algorithm for a single-source generalized shortest paths problem, also called the restricted generalized uncapacitated transshipment problem.  ...  Generalized Flow Approximation Schemes Using the strongly polynomial single-source generalized shortest paths algorithm (Algorithm 2), we develop fully polynomial-time approximation schemes for the generalized  ... 
doi:10.1006/jagm.2000.1130 fatcat:jperhhi5m5dthmt6yxccyochoi

Page 3698 of Mathematical Reviews Vol. , Issue 2002E [page]

2002 Mathematical Reviews  
Summary: “In this short paper we give a very simple fully poly- nomial approximation scheme for the restricted shortest path problem.  ...  (IL-TECH-E; Haifa); Raz, Danny (1-BELL; Murray Hill, NJ) A simple efficient approximation scheme for the restricted shortest path problem. (English summary) Oper. Res.  ... 

Literature Review

I. Youngster, M. Green
2013 Journal of the Pediatric Infectious Diseases Society  
This hierarchy allows for fast computation of approximate shortest paths for general graphs. The time-quality trade-off decision can be made at query time.  ...  For instance, general graphs require O(n3/2 ) space and constant query time for stretch 3 paths.  ...  Using dynamic programming and classical trimming techniques, we construct a fully polynomial-time approximation scheme for min-max regret shortest path.  ... 
doi:10.1093/jpids/pit078 pmid:26619506 fatcat:opm7qy3d3behjm6e36szpqzlim

Implementation Issues for the Reliable a Priori Shortest Path Problem

Xing Wu, Yu (Marco) Nie
2009 Transportation Research Record  
Because computational cost increases rapidly with T for the same resolution, the existing discretization scheme is not suitable for large networks.  ...  Using expected utility theory, Loui shows that, for polynomial functions, utility maximization is reduced to a class of bi-criteria shortest path problems that trade off mean and variance of random travel  ...  ACKNOWLEDGMENTS This research was funded in part by the Federal Highway Administration's University Transportation Center (UTC) program through the Center for the Commercialization of Innovative Transportation  ... 
doi:10.3141/2091-06 fatcat:nkdfgadzeza4zbqziojmbvsvym

Approximating Fractional Multicommodity Flow Independent of the Number of Commodities

Lisa K. Fleischer
2000 SIAM Journal on Discrete Mathematics  
We describe fully polynomial time approximation schemes for various multicommodity flow problems in graphs with m edges and n vertices.  ...  They are simple, deterministic, and for the versions without costs, they are strongly polynomial.  ...  We thank Cynthia Phillips for suggesting a simpler presentation of the maximum multicommodity flow algorithm, and Kevin Wayne, Jeffrey Oldham, and an anonymous referee for helpful comments.  ... 
doi:10.1137/s0895480199355754 fatcat:cxubrv77xbb6njqeet6sbiuc6q

Shortest Paths with Bundles and Non-additive Weights Is Hard [chapter]

Paul W. Goldberg, Antony McCabe
2013 Lecture Notes in Computer Science  
For the superadditive case we show that approximation with a factor of n for any > 0 is hard even when the subsets are of size at most 2.  ...  We show that if the owner is allowed to apply a non-additive pricing structure then the winner determination problem becomes NP-hard (in contrast with the quadratic time algorithm for the standard additive  ...  Theorem 4 . 4 No polynomial-time algorithm with an approximation ratio of less than n for any > 0 exists for SHORTEST PATH WITH SUPPLEMENTS unless P=NP. Proof.  ... 
doi:10.1007/978-3-642-38233-8_22 fatcat:qylj3sy4eva47i4vuhuw7ch5pu

Network protection with guaranteed recovery times using recovery domains

Greg Kuperman, Eytan Modiano
2013 2013 Proceedings IEEE INFOCOM  
This provides protection with guaranteed recovery times using up to 45% less protection resources than local recovery.  ...  This is in contrast to schemes that offer no recovery time guarantees, such as IP rerouting, or the prevalent local recovery scheme of Fast ReRoute, which often over-provisions resources to meet recovery  ...  The second is a fully polynomial time approximation scheme (FPTAS) that guarantees a solution to be within a factor of 1.5 of the optimal cost and 1.5(1 + ) of the maximum recovery time.  ... 
doi:10.1109/infcom.2013.6566855 dblp:conf/infocom/KupermanM13 fatcat:xpgzupbg3na7re7dacim6hvdue

Building Maximum Lifetime Shortest Path Data Aggregation Trees in Wireless Sensor Networks

Mengfan Shan, Guihai Chen, Dijun Luo, Xiaojun Zhu, Xiaobing Wu
2014 ACM transactions on sensor networks  
As shortest path spanning trees intuitively have short delay, it is imperative to find an energy-efficient shortest path tree for time-critical applications.  ...  We show that when restricted to shortest path trees, building maximum lifetime aggregation trees can be solved in polynomial time.  ...  Under this model, finding a shortest path aggregation tree with the maximum lifetime can be done in polynomial time.  ... 
doi:10.1145/2629662 fatcat:iqf23ejngba3dptig6wxhabavu

Minimum Delay Routing in Multihop Wireless Networks [chapter]

Maggie X. Cheng, Xuan Gong, Peng-Jun Wan
2011 Lecture Notes in Computer Science  
Along with throughput, end-to-end delay determines the user-experienced data transmission time. End-to-end delay refers to the total time it takes for a single packet to reach the destination.  ...  Since the actual delay depends on the MAC layer scheduling algorithm, at the network layer we try to reduce the interference on the path instead of the actual delay time.  ...  If there is no alternative path to link (i, j), then the distance is counted as ∞.  ... 
doi:10.1007/978-3-642-23490-3_13 fatcat:fj36ww6zgvahdep3snpqxvzpwy

Tunable QoS-aware network survivability

Jose Yallouz, Ariel Orda
2013 2013 Proceedings IEEE INFOCOM  
Then, we establish efficient algorithmic schemes for optimizing the level of survivability under additive end-to-end QoS bounds.  ...  Tunable survivability provides a quantitative measure for specifying the desired level (0%-100%) of survivability and offers flexibility in the choice of the routing paths.  ...  Approximation Schemes for Establishing QoS Aware Survivable Connections We proceed to establish Fully Polynomial Time Approximation Schemes (FPTAS) for the considered problems.  ... 
doi:10.1109/infcom.2013.6566883 dblp:conf/infocom/YallouzO13 fatcat:gwpx4ojjz5erxbgv3gzoku3bci

Shortest Path with Alternatives for Uniform Arrival Times: Algorithms and Experiments

Tim Nonner, Marco Laumanns, Marc Herbstritt
2014 Algorithmic Approaches for Transportation Modeling, Optimization, and Systems  
The Shortest Path with Alternatives (SPA) policy differs from classical shortest path routing in the following way: instead of providing an exact list of means of transportation to follow, this policy  ...  First, we show that an optimal policy of this type can be computed in polynomial time for uniform arrival times under reasonable assumptions.  ...  alternative at each stop, (P3) a shortest path with alternatives with an arbitrary number of alternatives at each stop.  ... 
doi:10.4230/oasics.atmos.2014.15 dblp:conf/atmos/NonnerL14 fatcat:2zgrp5grajbbvb7h4p6adaboyi

Generalized Unfoldings for Shortest Paths

Chanderjit Bajaj, T.T. Moh
1988 The international journal of robotics research  
For the special case when paths are constrained to the surfaces of 3-dimensional objects, simple planar unfoldings are used to obtain the shortest path.  ...  For the general case wben paths are tiot constrained to lie on any surface; we show the existence of generalized unfoldings wherein the shortest patb in 3-space again becomes a straight line.  ...  In Euclidean 2-space (the Euclidean plane) the problem is easy to solve and the shortest path is polynomial time computable. Lozano-Perez, Wesley [2] .  ... 
doi:10.1177/027836498800700105 fatcat:gz7rnskxqjadjfjx7gtfzxeva4

Evolutionary Algorithms For The Multiobjective Shortest Path Problem

José Maria A. Pangilinan, Gerrit K. Janssens
2007 Zenodo  
Results show that the evolutionary algorithm can find diverse solutions to the MSPP in polynomial time (based on several network instances) and can be an alternative when other methods are trapped by the  ...  This paper presents an overview of the multiobjective shortest path problem (MSPP) and a review of essential and recent issues regarding the methods to its solution.  ...  For instance, Hansen [8] and Warburton [9] separately develop fully polynomial time approximation schemes (FPTAS) for finding paths that are approximately Pareto-optimal.  ... 
doi:10.5281/zenodo.1079535 fatcat:plsqsotxmfbznf7tuel7zcfwnq
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