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## Filters

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Flows with unit path capacities and related packing and covering problems

2009
*
Journal of combinatorial optimization
*

We derive several

doi:10.1007/s10878-009-9225-x
fatcat:on5fprvm6batpbvh54qdpsj7jq
*results**on*the complexity and approximability*of*the*new*problem. ...*On*the way we also discover two closely related basic covering and*packing*problems that are*of*independent interest. ... In D the*new**path*uses the arc from v to w and then the arcs corresponding to the*ones*P used in D after (v, w). Let the*resulting*s-t -flow be denoted byx. ...##
###
Node-Capacitated Ring Routing

2002
*
Mathematics of Operations Research
*

*A*relation

*of*the problem to its edge-

*capacitated*counterpart will also be explained. ... Our approach gives rise to

*a*combinatorial, strongly polynomial algorithm to compute either

*a*violating double-cut or

*a*

*node*-

*capacitated*multicommodity flow. ... Therefore it is no wonder that there are many more

*results*

*on*edge-

*capacitated*routing problems while our knowledge

*on*

*node*-disjoint or

*node*-

*capacitated*

*paths*problem is much more limited. ...

##
###
On the interaction between power-aware FPGA CAD Algorithms

2003
*
ICCAD-2003. International Conference on Computer Aided Design (IEEE Cat. No.03CH37486)
*

In this paper, we focus

doi:10.1109/iccad.2003.159755
fatcat:553bhrgdizfhvl62jlt6vz63cy
*on*FPGA CAD tools. Specifically, we describe*a**new*power-aware CAD flow for FPGAs that was developed to answer the above questions. ... The majority*of*the overall savings were achieved during the technology mapping and clustering stages*of*the poweraware FPGA CAD flow. ... In the original algorithm,*one**of*the LUTs*on*the most time-critical*path*is chosen. The second attraction function selects*a*LUT to be*packed*into*a*partially filled cluster. ...##
###
An Algorithm for Node-Capacitated Ring Routing
[chapter]

2005
*
Lecture Notes in Computer Science
*

*A*strongly polynomial time algorithm is described to solve the

*node*-

*capacitated*routing problem in an undirected ring network.

*A*routing is an (integral)

*packing*

*of*

*paths*in

*a*graph. ...

*A*routing problem has the following input:

*a*graph, nonnegative demands between the pairs

*of*vertices, and capacities

*of*

*some*resources (edges or

*nodes*). ... Note that the

*node*-

*capacitated*routing problem is more general than the edgecapacitated

*one*. To see this, put

*a*

*new*

*node*

*on*each edge, and assign the original capacity

*of*the edge to this

*new*

*node*. ...

##
###
An algorithm for node-capacitated ring routing

2007
*
Operations Research Letters
*

*A*strongly polynomial time algorithm is described to solve the

*node*-

*capacitated*routing problem in an undirected ring network.

*A*routing is an (integral)

*packing*

*of*

*paths*in

*a*graph. ...

*A*routing problem has the following input:

*a*graph, nonnegative demands between the pairs

*of*vertices, and capacities

*of*

*some*resources (edges or

*nodes*). ... Note that the

*node*-

*capacitated*routing problem is more general than the edgecapacitated

*one*. To see this, put

*a*

*new*

*node*

*on*each edge, and assign the original capacity

*of*the edge to this

*new*

*node*. ...

##
###
Odd Path Packings

1989
*
European journal of combinatorics (Print)
*

An odd

doi:10.1016/s0195-6698(89)80075-7
fatcat:wkhrjytkebg2vbgcqd6dt4wypi
*path**packing*in*a*graph is*a*collection*of*edge-disjoint odd length*paths*such that each*node*is an end*node**of*at most*one**path*. ... We consider the problem*of*finding such*a**packing*for which the number*of**paths*is maximum. ... An odd*path**packing*, or simply*a**packing*, is*a*set*of*edge-disjoint odd length*paths*such that each*node*is an end*of*at most*one**path*. However,*a**node*may be an internal*node**of*any number*of**paths*. ...##
###
Path Cover and Path Pack Inequalities for the Capacitated Fixed-Charge Network Flow Problem

2017
*
SIAM Journal on Optimization
*

These inequalities are based

doi:10.1137/15m1033009
fatcat:nob434lo6jef7jtb2igkftqb4m
*on*an explicit characterization*of*the submodular inequalities through*a*fast computation*of*parametric minimum cuts*on**a**path*, and they generalize the well-known flow cover ... and flow*pack*inequalities for the single-*node*relaxations*of*fixed-charge flow models. ... Acknowledgements*A*. ...##
###
An Improved Algorithm for Packing T-Paths in Inner Eulerian Networks
[chapter]

2012
*
Lecture Notes in Computer Science
*

This paper concerns the problem

doi:10.1007/978-3-642-32241-9_10
fatcat:p4ns4uu2nbdj3gv63h2u2alt74
*of*finding*a*maximum T -*path**packing*, i.e.*a*maximum collection*of*arc-disjoint T -*paths*.*A*min-max relation for this problem was established by Lomonosov. ... By*a*T -*path*we mean*a*simple directed*path*connecting distinct terminals with all intermediate*nodes*in V −T . ... T -*path**packing*problem in*a**capacitated*digraph (V, E). ...##
###
Path Cover and Path Pack Inequalities for the Capacitated Fixed-Charge Network Flow Problem
[article]

2017
*
arXiv
*
pre-print

These inequalities are based

arXiv:1705.05920v1
fatcat:ioxh43msmvfmdfhdjaeyhacm2m
*on*an explicit characterization*of*the submodular inequalities through*a*fast computation*of*parametric minimum cuts*on**a**path*, and they generalize the well-known flow cover ... and flow*pack*inequalities for the single-*node*relaxations*of*fixed-charge flow models. ... Acknowledgements*A*. ...##
###
Power and area optimization by reorganizing CMOS complex gate circuits

1995
*
Proceedings of the 1995 international symposium on Low power design - ISLPED '95
*

Transistor sizing and layout are interdependent, the optimization

doi:10.1145/224081.224109
dblp:conf/islped/TachibanaKNKYMG95
fatcat:4546igmcdfcrnes6zezgtgrzvm
*of**one**results*in the optimization*of*the other. ... This paper proposes*a*method for achieving low-power control-logic modules using*a*combination*of*CMOS complex gate reorganization, transistor size optimization, and transistor layout. ... If there is another route shorter than the original*one*, the*new*wiring*path*will pass through the shorter route,*resulting*in*a*shorter wire length. ...##
###
Multi-resource Energy-efficient Routing in Cloud Data Centers with Networks-as-a-Service
[article]

2016
*
arXiv
*
pre-print

routing

arXiv:1501.05086v2
fatcat:djg2aqqnwzglxcyrlbftq6g75a
*paths*are assigned based*on*the distributions*of*both*node*residual capacities and flow demands. ... By leveraging the structural regularity*of*data center networks, we also provide*a*fast topology-aware heuristic method based*on*hierarchically solving*a*series*of*vector bin*packing*instances. ... As*a**result*, we have to keep (almost) the same reservation across each type*of*resource*on*every*node**on*the*path*for each flow. ...##
###
A note on packing paths in planar graphs

1995
*
Mathematical programming
*

Here we generalize this

doi:10.1007/bf01585937
fatcat:a5njs2efrjhojfipc66snef55i
*result*by showing how*a*natural strengthening*of*the cut criterion yields better*packings**of**paths*. ... The main*result*is derived from*a*theorem*of**A*. Seb} o*on*the structure*of*1 weightings*of**a*bipartite graph with no negative circuits. ... Then for each*node*v 2 (V (K i ) : i = 1; : : : ; k) split v into two in the following sense: add*a**new*copy v 0*of*v, called*a*split*node*, to the graph, along with*a**new*edge v 0 v, called*a*split edge ...##
###
Connected bin packing problem on traceable graphs

2022
*
Iranian journal of numerical analysis and optimization
*

We consider

doi:10.22067/ijnao.2021.67913.1010
doaj:4f3fe01ed77b4c8d87a8f6b817f43626
fatcat:iljmepolszhqzlhykwbwstakka
*a**new*extension*of*the bin*packing*problem in which*a*set*of*connectivity constraints should be satisfied. An undirected graph with*a*weight function*on*the*nodes*is given. ... The objective is to*pack*all the*nodes*in the minimum number*of*unit-capacity bins, such that the induced subgraph*on*the set*of**nodes**packed*in each bin is connected. ... CBPP*on*traceable graphs*A*Hamiltonian*path*is*a**path*that visits each*node**of*the graph exactly once.*A*traceable graph is*a*graph possessing*a*Hamiltonian*path*. ...##
###
Page 9407 of Mathematical Reviews Vol. , Issue 2004k
[page]

2004
*
Mathematical Reviews
*

In addition

*a*bundle method is used to solve the Lagrangean dual at each*node*. Computational*results**on**some*variants*of*the branch-and-bound method are given and compared. ... Distances between unconnected*nodes*and*nodes*in the subtree ¢ can be defined*on**paths*that are restricted to lie in the larger tree T (the restricted case), or can be defined*on**paths*in an auxiliary ...##
###
Page 8299 of Mathematical Reviews Vol. , Issue 2000k
[page]

2000
*
Mathematical Reviews
*

The idea behind the algorithm is to control two
parameters in order to construct

*a*feasible (with respect to the*path*delays and the number*of*Steiner*nodes*) tree*of*small cost. ... the num- ber*of*Steiner*nodes*. ...
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