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Approximation Algorithms for Orienting Mixed Graphs
[chapter]

2011
*
Lecture Notes in Computer Science
*

When the input

doi:10.1007/978-3-642-21458-5_35
fatcat:oefqitkwnrfcfc5cuzvzbbwivu
*graph*is undirected, a sub-logarithmic*approximation*is known*for*the problem. ... Here we give the first*approximation**algorithm*to this problem. Our*algorithm*provides a sub-linear guarantee in the general case, and logarithmic guarantees*for*structured instances. ... The known upper and lower bounds*for*the*approximation*ratio of maximum-*mixed*-*graph*-*orientation*are far from being tight. ...##
###
Approximation algorithms for orienting mixed graphs

2013
*
Theoretical Computer Science
*

When the input

doi:10.1016/j.tcs.2012.03.044
fatcat:xnlp26mjlnaermoav5xzh3wl4i
*graph*is undirected, a sub-logarithmic*approximation*is known*for*the problem. ... Here we give the first*approximation**algorithm*to this problem. Our*algorithm*provides a sub-linear guarantee in the general case, and logarithmic guarantees*for*structured instances. ... The known upper and lower bounds*for*the*approximation*ratio of maximum-*mixed*-*graph*-*orientation*are far from being tight. ...##
###
Improved Approximation for Orienting Mixed Graphs
[article]

2012
*
arXiv
*
pre-print

This property enables us to modify the best known

arXiv:1204.0219v1
fatcat:ki5fsv74mrcrbdh2sktyxl6fd4
*algorithms**for*maximum*mixed**graph**orientation*and some of its special structured instances, due to Elberfeld et al. ... An instance of the maximum*mixed**graph**orientation*problem consists of a*mixed**graph*and a collection of source-target vertex pairs. ... Improved*Approximation**for*The General Case In this section, we develop a relatively simple Ω(1/(n|P |) 1/3 )-*approximation**algorithm**for*the maximum*mixed**graph**orientation*problem. ...##
###
Steiner Forest Orientation Problems
[article]

2012
*
arXiv
*
pre-print

*orientation*D with P[D]=P (

*for*undirected

*graphs*this problem admits a polynomial time

*algorithm*

*for*any P, but it is NP-complete on

*mixed*

*graphs*). ... The goal is to find a minimum-cost subgraph H of G and an

*orientation*D of H such that P[D]=P. We give a 4-

*approximation*

*algorithm*

*for*this problem. ... Our main results are a 4-

*approximation*

*algorithm*

*for*Steiner Forest

*Orientation*, an n O(|P |) time

*algorithm*

*for*P -

*Orientation*on

*mixed*

*graphs*, and an O(n + m) + 2 O(k·log log k) time

*algorithm*

*for*k ...

##
###
Steiner Forest Orientation Problems

2013
*
SIAM Journal on Discrete Mathematics
*

P [D] = P (

doi:10.1137/120883931
fatcat:ureqxrwvbbebtanazizlaylpoy
*for*undirected*graphs*this problem admits a polynomial time*algorithm**for*any P , but it is NP-complete on*mixed**graphs*). ... The goal is to find a minimum-cost subgraph H of G and an*orientation*D of H such that P [D] = P . We give a 4-*approximation**algorithm**for*this problem. ... Our main results are a 4-*approximation**algorithm**for*Steiner Forest*Orientation*, an n O(|P |) time*algorithm**for*P -*Orientation*on*mixed**graphs*, and an O(n + m) + 2 O(k·log log k) time*algorithm**for*k ...##
###
Steiner Forest Orientation Problems
[chapter]

2012
*
Lecture Notes in Computer Science
*

P [D] = P (

doi:10.1007/978-3-642-33090-2_32
fatcat:n2kba5uohvbrhe4bb2satekw24
*for*undirected*graphs*this problem admits a polynomial time*algorithm**for*any P , but it is NP-complete on*mixed**graphs*). ... The goal is to find a minimum-cost subgraph H of G and an*orientation*D of H such that P [D] = P . We give a 4-*approximation**algorithm**for*this problem. ... Our main results are a 4-*approximation**algorithm**for*Steiner Forest*Orientation*, an n O(|P |) time*algorithm**for*P -*Orientation*on*mixed**graphs*, and an O(n + m) + 2 O(k·log log k) time*algorithm**for*k ...##
###
Improved Orientations of Physical Networks
[chapter]

2010
*
Lecture Notes in Computer Science
*

We develop an

doi:10.1007/978-3-642-15294-8_18
fatcat:zzqmck6bgng25kiffniy5gjwlu
*approximation**algorithm**for*this problem with a performance guarantee of O(log n/ log log n). This result improves on a previous logarithmic*approximation*, due to Medvedovsky et al. ... In addition, motivated by interactions whose direction is pre-set such as protein-DNA interactions, we extend our*algorithm*to handle*mixed**graphs*, a major open problem posed by earlier work. ... Acknowledgments: The authors would like to thank Yael Silberberg*for*her help in gathering statistics on the KEGG pathways. ...##
###
Oriented Coloring: Complexity and Approximation
[chapter]

2006
*
Lecture Notes in Computer Science
*

Finally, we investigate the

doi:10.1007/11611257_20
fatcat:tkgzlnsnxfgczjw6v3a44g55bm
*approximation*of this problem: both positive and negative results are devised. ... This paper is devoted to an*oriented*coloring problem motivated by a task assignment model. ... Acknoledgement We are grateful to ananymous referees*for*their helpful comments. ...##
###
Inferring protein-protein interaction and protein-DNA interaction directions based on cause-effect pairs in undirected and mixed networks
[article]

2017
*
arXiv
*
pre-print

In the

arXiv:1706.00911v1
fatcat:ozt5w7satfajjpza44g2r6fr64
*mixed*case, we present polynomial-time*algorithms**for*the problem on paths and cycles, and an FPT-*algorithm*based on the combined parameter the number of arcs and the number of pairs on general ... This is called maximum*graph**orientation*problem, and has applications in understanding interactions in protein-protein interaction networks and protein-DNA interaction networks. ... and*mixed**graphs*. ...##
###
Parallel Batch-Dynamic Algorithms for k-Core Decomposition and Related Graph Problems

2022
*
Proceedings of the 34th ACM Symposium on Parallelism in Algorithms and Architectures
*

As a by-product, our 𝑘-core decomposition

doi:10.1145/3490148.3538569
fatcat:pibyp63wbfbgfiu6odh7mepyzu
*algorithm*also gives a batch-dynamic*algorithm**for*maintaining an 𝑂 (𝛼) out-degree*orientation*, where 𝛼 is the current arboricity of the*graph*. ... Given a*graph*with 𝑛 vertices and a batch of updates B, our*algorithm*provably maintains a (2 + 𝜀)-*approximation*of the coreness values of all vertices (*for*any constant 𝜀 > 0) in 𝑂 (|B| log 2 𝑛) ...*For*all but the smallest*graphs*, PLDSOpt obtains 2.22-13.09×, 5.56-19.64×, and 4.4-121.76× speedups over the fastest static*algorithm**for*each*graph**for*Ins, Del, and*Mix*, respectively. ...##
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A GRASP heuristic for the mixed Chinese postman problem

2002
*
European Journal of Operational Research
*

In this paper, we present a heuristic

doi:10.1016/s0377-2217(01)00296-x
fatcat:np4le7j6hzfa5npxrpg2hkpipu
*algorithm**for*this problem, the so-called*Mixed*CPP (MCPP), based on GRASP -Greedy Randomized Adaptive Search Proceduretechniques. ... However, if we deal with a*mixed**graph*(having edges and arcs), the problem turns out to be N P-hard. ... If all the edges in the*mixed**graph*are*oriented*, then the*graph*can be considered as a directed*graph*. ...##
###
On the Number of Eulerian Orientations of a Graph

1996
*
Algorithmica
*

Our

doi:10.1007/s004539900057
fatcat:fgemqnxmvvaylacrfjog3gyewe
*algorithms*are based on a reduction to sampling and*approximately*counting perfect matchings*for*a class of*graphs**for*which the methods of Broder [3,10] and others [4,6] apply. ... We give efficient randomized schemes to sample and*approximately*count Eulerian*orientations*of any Eulerian*graph*. ... Our*algorithms*are based on a reduction to sampling and*approximately*counting perfect matchings*for*a class of*graphs**for*which the methods of Broder [3, 10] and others [4, 6] apply. ...##
###
Page 675 of Mathematical Reviews Vol. , Issue 2004a
[page]

2004
*
Mathematical Reviews
*

*for*the

*mixed*Chinese postman problem. ... While the corresponding problems

*for*undirected

*graphs*and directed

*graphs*(UCPP and DCPP) have efficient polynomial

*algorithms*, the MCPP is known to be NP-complete. ...

##
###
Optimally Orienting Physical Networks
[chapter]

2011
*
Lecture Notes in Computer Science
*

In a network

doi:10.1007/978-3-642-20036-6_39
fatcat:occm7yjcenczrps2ddka7p452y
*orientation*problem one is given a*mixed**graph*, consisting of directed and undirected edges, and a set of source-target vertex pairs. ... This problem is NP-complete and no*approximation**algorithms*are known*for*it. It arises in the context of analyzing physical networks of protein-protein and protein-DNA interactions. ... An ILP*Algorithm**for**Orienting**Mixed**Graphs*In this section we present an integer linear program (ILP)*for*optimally*orienting*a*mixed**graph*. ...##
###
Optimally Orienting Physical Networks

2011
*
Journal of Computational Biology
*

In a network

doi:10.1089/cmb.2011.0163
pmid:21999286
fatcat:ykdvlozy75ekrjfrenajryq764
*orientation*problem one is given a*mixed**graph*, consisting of directed and undirected edges, and a set of source-target vertex pairs. ... This problem is NP-complete and no*approximation**algorithms*are known*for*it. It arises in the context of analyzing physical networks of protein-protein and protein-DNA interactions. ... An ILP*Algorithm**for**Orienting**Mixed**Graphs*In this section we present an integer linear program (ILP)*for*optimally*orienting*a*mixed**graph*. ...
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