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Flows with unit path capacities and related packing and covering problems

Maren Martens, Martin Skutella
2009 Journal of combinatorial optimization  
We derive several 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.  ... 
doi:10.1007/s10878-009-9225-x fatcat:on5fprvm6batpbvh54qdpsj7jq

Node-Capacitated Ring Routing

András Frank, Bruce Shepherd, Vivek Tandon, Zoltán Végh
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.  ... 
doi:10.1287/moor.27.2.372.323 fatcat:th6tfb7mevdr3ekkbd57gape44

On the interaction between power-aware FPGA CAD Algorithms

J. Lamoureux, S.J.E. Wilton
2003 ICCAD-2003. International Conference on Computer Aided Design (IEEE Cat. No.03CH37486)  
In this paper, we focus 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.  ... 
doi:10.1109/iccad.2003.159755 fatcat:553bhrgdizfhvl62jlt6vz63cy

An Algorithm for Node-Capacitated Ring Routing [chapter]

András Frank, Zoltán Király, Balázs Kotnyek
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.  ... 
doi:10.1007/11561071_24 fatcat:5dlmod3p3bgw3gckt6kbuus7fa

An algorithm for node-capacitated ring routing

András Frank, Zoltán Király, Balázs Kotnyek
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.  ... 
doi:10.1016/j.orl.2006.03.015 fatcat:ktsmoyw4urhkve6j54mbdzreyy

Odd Path Packings

W.R. Pulleyblank, D. De Werra
1989 European journal of combinatorics (Print)  
An odd 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.  ... 
doi:10.1016/s0195-6698(89)80075-7 fatcat:wkhrjytkebg2vbgcqd6dt4wypi

Path Cover and Path Pack Inequalities for the Capacitated Fixed-Charge Network Flow Problem

Alper Atamtürk, Simge Küçükyavuz, Birce Tezel
2017 SIAM Journal on Optimization  
These inequalities are based 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.  ... 
doi:10.1137/15m1033009 fatcat:nob434lo6jef7jtb2igkftqb4m

An Improved Algorithm for Packing T-Paths in Inner Eulerian Networks [chapter]

Maxim A. Babenko, Kamil Salikhov, Stepan Artamonov
2012 Lecture Notes in Computer Science  
This paper concerns the problem 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).  ... 
doi:10.1007/978-3-642-32241-9_10 fatcat:p4ns4uu2nbdj3gv63h2u2alt74

Path Cover and Path Pack Inequalities for the Capacitated Fixed-Charge Network Flow Problem [article]

Alper Atamturk, Birce Tezel, Simge Kucukyavuz
2017 arXiv   pre-print
These inequalities are based 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.  ... 
arXiv:1705.05920v1 fatcat:ioxh43msmvfmdfhdjaeyhacm2m

Power and area optimization by reorganizing CMOS complex gate circuits

M. Tachibana, S. Kurosawa, R. Nojima, N. Kojima, M. Yamada, T. Mitsuhashi, N. Goto
1995 Proceedings of the 1995 international symposium on Low power design - ISLPED '95  
Transistor sizing and layout are interdependent, the optimization 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.  ... 
doi:10.1145/224081.224109 dblp:conf/islped/TachibanaKNKYMG95 fatcat:4546igmcdfcrnes6zezgtgrzvm

Multi-resource Energy-efficient Routing in Cloud Data Centers with Networks-as-a-Service [article]

Lin Wang, Antonio Fernández Anta, Fa Zhang, Jie Wu, Zhiyong Liu
2016 arXiv   pre-print
routing 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.  ... 
arXiv:1501.05086v2 fatcat:djg2aqqnwzglxcyrlbftq6g75a

A note on packing paths in planar graphs

András Frank, Zoltán Szigeti
1995 Mathematical programming  
Here we generalize this 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  ... 
doi:10.1007/bf01585937 fatcat:a5njs2efrjhojfipc66snef55i

Connected bin packing problem on traceable graphs

A. Nejoomi, A. Dolati
2022 Iranian journal of numerical analysis and optimization  
We consider 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.  ... 
doi:10.22067/ijnao.2021.67913.1010 doaj:4f3fe01ed77b4c8d87a8f6b817f43626 fatcat:iljmepolszhqzlhykwbwstakka

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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