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Two-Commodity Flow is Equivalent to Linear Programming under Nearly-Linear Time Reductions
[article]

2022

We give a

doi:10.48550/arxiv.2201.11587
fatcat:dgmhdo3ennc43m4zuldf44biqa
*nearly*-*linear**time**reduction*that encodes any*linear**program*as a 2-*commodity**flow*problem with only a small blow-up in size. ... We remark that our*reduction*does not run in strongly polynomial*time*and that it*is*open whether 2-*commodity**flow*and*linear**programming*are*equivalent*in strongly polynomial*time*. ... In*nearly*-*linear**time*, we can convert this*linear**program**to*a 2-*commodity**flow*problem which*is*feasible if and only if the original*program**is*. ...##
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Two-Commodity Flow Is Equivalent to Linear Programming Under Nearly-Linear Time Reductions

2022

We give a

doi:10.4230/lipics.icalp.2022.54
fatcat:2d67cqhafvfz5omjy54cmzdrly
*nearly*-*linear**time**reduction*that encodes any*linear**program*as a 2-*commodity**flow*problem with only a small blow-up in size. ... We remark that our*reduction*does not run in strongly polynomial*time*and that it*is*open whether 2-*commodity**flow*and*linear**programming*are*equivalent*in strongly polynomial*time*. ... Concretely, they showed that the*linear*equations that arise I C A L P 2 0 2 2 54:4*Two*-*Commodity**Flow**Is**Equivalent**to**Linear**Programming*in interior point methods for multi-*commodity**flow*are as hard ...##
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A Dual-Ascent Procedure for Large-Scale Uncapacitated Network Design

1989
*
Operations Research
*

He shows that asymptotically it

doi:10.1287/opre.37.5.716
fatcat:6kuknncc5nbzxbnh2veqawlkjm
*is*very likely that the cost of the solution generated by this heuristic will,*under*certain conditions, be very close*to*the cost of the optimal solution. ... Section 2 describes dual ascent procedures for computing approximate solutions*to*the dual of the*linear**programming*relaxation of the design problem formulation. ... We would like*to*thank Professor Bruce W. Lamar for providing us the data for the Less-than-Truckload Consolidation test problems. ...##
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Multicommodity flow problems with a bounded number of paths: A flow deviation approach

2006
*
Networks
*

A heuristic control of the path generation

doi:10.1002/net.20143
fatcat:boiy5nwpczcq7b5n4djn4hqn5q
*is*then embedded in the original algorithm based on the concepts of cleaning the quasi inactive paths and the*reduction*of the*flow*width for each*commodity*. ... We propose a modified version of the*Flow*Deviation method of Fratta, Gerla and Kleinrock*to*solve multicommodity problems with minimal congestion and a bounded number of active paths. ... This basic problem*is*known*to*be hard*to*solve even if it can be written as a*linear**program*. ...##
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Hardness Results for Structured Linear Systems
[article]

2017
*
arXiv
*
pre-print

We show that if the

arXiv:1705.02944v2
fatcat:stpvkn7jbrgk3p4utcfrtq34nu
*nearly*-*linear**time*solvers for Laplacian matrices and their generalizations can be extended*to*solve just slightly larger families of*linear*systems, then they can be used*to*quickly ... can solve in*nearly*-*linear**time*will soon halt. ...*commodity**flows**to*(1+ ) accuracy in*time*that scales as poly( −1 ) [GK98, Mad10, Fle00, LMP + 91], even obtaining*nearly*-*linear*running*times*when the graph*is*undirected [She13, KLOS14, Pen16] . ...##
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On Choosing an Optimal Technology

1967
*
Management science
*

There

doi:10.1287/mnsc.13.5.413
fatcat:fi2gvute5bgylkhbailvdd6n4a
*is*no joint production. Each hoinogeneous*commodity**is*produced or purchased by*linear*processes or activities with fixed coefficients. ... The question of which*commodities*are*to*be considered exogenous*is*entirely relative*to*the particular production system*under*consideration. 2 In the case of circulating capital (intermediate materials ... The special structure of the problem*under*investigation allows us*to*perform such a*reduction*in this particular case. ...##
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Using life cycle assessment and techno-economic analysis in a real options framework to inform the design of algal biofuel production facilities

2017
*
Bioresource Technology
*

*To*do this, an existing LCA/TEA model

*is*paired with a mixed integer

*linear*

*program*(MILP) and subjected

*to*

*time*-varying data for key operational parameters (e.g., prices for electricity, natural gas, ... (profits are maximized) via a mixed integer

*linear*

*program*(MILP). ...

##
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Stronger Bounds on Braess's Paradox and the Maximum Latency of Selfish Routing

2011
*
SIAM Journal on Discrete Mathematics
*

Finally, we use our family of

doi:10.1137/090769600
fatcat:63cvtfzcvfanhntvaeua6vvupy
*two*-*commodity*networks*to*exhibit a natural network design problem with intrinsically exponential (in)approximability. ... In multicommodity networks, we exhibit an infinite family of*two*-*commodity*networks, related*to*the Fibonacci numbers, in which both the worst-case severity of Braess's Paradox and the price of anarchy ... We define our notion of*equivalence*so that Lemma 6.1 ensures that the*linear**program*has a bounded maximum, and then analyze the vertices of the feasible region of the*linear**program**to*derive the following ...##
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Water use and salinity in the Murray?Darling Basin: A state-contingent model

2007
*
Australian Journal of Agricultural and Resource Economics
*

The object of the present paper

doi:10.1111/j.1467-8489.2007.00380.x
fatcat:oz6xguppjfbxfekx7673rwgco4
*is**to*show how the*linear*and non-*linear**programming*models commonly used in modelling problems such as those arising in the Murray-Darling Basin may be adapted*to*incorporate ... The supply of water for irrigation*is*subject*to*climatic and policy uncertainty. ... By the*time*a limit, know as the Cap, was imposed on diversions in 1995, prohibiting further growth in average annual allocations,*nearly*100 per cent of normally available*flows*had been allocated, and ...##
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Multi-hop Routing and Scheduling in Wireless Networks in the SINR Model
[chapter]

2012
*
Lecture Notes in Computer Science
*

For

doi:10.1007/978-3-642-28209-6_16
fatcat:ir2fv5pabvcdja6n76zvjswdee
*linear*powers, Wan et al. [WFJ + 11] obtain a O(log n)-approximation for THROUGHPUT-ROUTE. The algorithm*is*based on a*reduction**to*the single-slot problem using the ellipsoid method. ... Every bucket consists of a set of links that have*nearly**equivalent*reception powers. We denote the number of nonempty buckets by σ. ... The*linear**program*formulation that we use for computing the multi-*commodity**flow*f*is*as follows. ...##
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Achieving Target Equilibria in Network Routing Games without Knowing the Latency Functions
[article]

2014
*
arXiv
*
pre-print

We show that,

arXiv:1408.1429v1
fatcat:rhap5mhmfnbzjc7hxcadekwmx4
*under*fairly general settings, one can efficiently compute edge tolls that induce a given target multicommodity*flow*in a nonatomic routing game using a polynomial number of queries*to*an ... We obtain tighter bounds on the query complexity for series-parallel networks, and single-*commodity*routing games with*linear*latency functions, and complement these with a query-complexity lower bound ... Each query*is*a Stackelberg routing, which*is*a*flow*of volume at most α*times*the total volume, and returns the equilibrium*flow**under*this Stackelberg routing. ...##
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Achieving Target Equilibria in Network Routing Games without Knowing the Latency Functions

2014
*
2014 IEEE 55th Annual Symposium on Foundations of Computer Science
*

We show that,

doi:10.1109/focs.2014.12
dblp:conf/focs/BhaskarLSS14
fatcat:gdqccw6bpngrvcibok2zyrevpm
*under*fairly general settings, one can efficiently compute edge tolls that induce a given target multicommodity*flow*in a nonatomic routing game using a polynomial number of queries*to*an ... We obtain tighter bounds on the query complexity for series-parallel networks, and single-*commodity*routing games with*linear*latency functions, and complement these with a query-complexity lower bound ... Each query*is*a Stackelberg routing, which*is*a*flow*of volume at most α*times*the total volume, and returns the equilibrium*flow**under*this Stackelberg routing. ...##
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Outdoor Downward-Facing Optical Flow Odometry with Commodity Sensors
[chapter]

2010
*
Springer Tracts in Advanced Robotics
*

A common tactic in such cases

doi:10.1007/978-3-642-13408-1_17
fatcat:fcn36ghky5d7tbat3pqsi35b34
*is**to*position visually, and we present a visual odometry implementation with the unusual reliance on optical mouse sensors*to*report vehicle velocity. ... at*times*more accurate than that achievable by wheel odometry and visibly more desirable for perception purposes than that provided by a high-end GPS-INS system. ... Acknowledgements This research was supported in part by NASA*under*grants, NNX07AE30G, John Caruso, Project Manager, and NNX08AJ99G, Robert Ambrose,*Program*Scientist. ...##
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Hardness Results for Laplacians of Simplicial Complexes via Sparse-Linear Equation Complete Gadgets
[article]

2022
*
arXiv
*
pre-print

We prove this by a

arXiv:2202.05011v1
fatcat:uywzjonex5bdxh4noylvuplyl4
*nearly*-*linear**time**reduction*from general*linear*equations*to*combinatorial Laplacians of 2-complexes. ... It*is*known that*nearly*-*linear**time*solvers exist for graph Laplacians. However,*nearly*-*linear**time*solvers for combinatorial Laplacians are only known for restricted classes of complexes. ... Therefore, the*two*-step*reduction**is*a*nearly*-*linear**time**reduction*while the one-step*reduction**is*not. • Why encode into a 2-complex rather than a 1-complex? ...##
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Optimisation in Forest Management

2016
*
Current Forestry Reports
*

These approaches continue

doi:10.1007/s40725-016-0027-y
fatcat:4hwmuvxuyfhxzekdqkn5sexnre
*to*evolve, and in the last 5 years, the research has expanded*to*demonstrate how complex, non-*linear*relationships can be recognised and incorporated into planning processes at ... Through this review, we found that landscape-level optimisation*is*a relatively new and expanding area of research, most often performed by one large public landowner in regions where the resulting plan ... [81] developed a*linear**programming*model*to*minimise harvest*reductions*due*to*losses from an insect infestation while imposing a wood*flow*constraint. ...
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