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

2006
*
Lecture Notes in Computer Science
*

Applying this

doi:10.1007/11809678_45
fatcat:xhxydjkcibdajbl2z6tnzdptle
*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 ...##
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An FPTAS for the Knapsack Problem with Parametric Weights
[article]

2017
*
arXiv
*
pre-print

We present the first fully

arXiv:1703.06048v1
fatcat:nyosa2im6vfwve2276nlyqicc4
*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. ...##
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Combinatorial Approximation Algorithms for Generalized Flow Problems

2001
*
Journal of Algorithms
*

Using this generalized

doi:10.1006/jagm.2000.1130
fatcat:jperhhi5m5dthmt6yxccyochoi
*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 ...##
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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. ...##
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Literature Review

2013
*
Journal of the Pediatric Infectious Diseases Society
*

This hierarchy allows

doi:10.1093/jpids/pit078
pmid:26619506
fatcat:opm7qy3d3behjm6e36szpqzlim
*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*. ...##
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Implementation Issues for the Reliable a Priori Shortest Path Problem

2009
*
Transportation Research Record
*

Because computational cost increases rapidly

doi:10.3141/2091-06
fatcat:nkdfgadzeza4zbqziojmbvsvym
*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 ...##
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Approximating Fractional Multicommodity Flow Independent of the Number of Commodities

2000
*
SIAM Journal on Discrete Mathematics
*

We describe fully

doi:10.1137/s0895480199355754
fatcat:cxubrv77xbb6njqeet6sbiuc6q
*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. ...##
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Shortest Paths with Bundles and Non-additive Weights Is Hard
[chapter]

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. ...

##
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Network protection with guaranteed recovery times using recovery domains

2013
*
2013 Proceedings IEEE INFOCOM
*

This provides protection

doi:10.1109/infcom.2013.6566855
dblp:conf/infocom/KupermanM13
fatcat:xpgzupbg3na7re7dacim6hvdue
*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*. ...##
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Building Maximum Lifetime Shortest Path Data Aggregation Trees in Wireless Sensor Networks

2014
*
ACM transactions on sensor networks
*

As

doi:10.1145/2629662
fatcat:iqf23ejngba3dptig6wxhabavu
*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*. ...##
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Minimum Delay Routing in Multihop Wireless Networks
[chapter]

2011
*
Lecture Notes in Computer Science
*

Along

doi:10.1007/978-3-642-23490-3_13
fatcat:fj36ww6zgvahdep3snpqxvzpwy
*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 ∞. ...##
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Tunable QoS-aware network survivability

2013
*
2013 Proceedings IEEE INFOCOM
*

Then, we establish efficient algorithmic

doi:10.1109/infcom.2013.6566883
dblp:conf/infocom/YallouzO13
fatcat:gwpx4ojjz5erxbgv3gzoku3bci
*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. ...##
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Shortest Path with Alternatives for Uniform Arrival Times: Algorithms and Experiments

2014
*
Algorithmic Approaches for Transportation Modeling, Optimization, and Systems
*

The

doi:10.4230/oasics.atmos.2014.15
dblp:conf/atmos/NonnerL14
fatcat:2zgrp5grajbbvb7h4p6adaboyi
*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. ...##
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Generalized Unfoldings for Shortest Paths

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] . ...

##
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Evolutionary Algorithms For The Multiobjective Shortest Path Problem

2007
*
Zenodo
*

Results show that the evolutionary algorithm can find diverse solutions to the MSPP in

doi:10.5281/zenodo.1079535
fatcat:plsqsotxmfbznf7tuel7zcfwnq
*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. ...
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