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### Approximation Algorithms for Orienting Mixed Graphs [chapter]

Michael Elberfeld, Danny Segev, Colin R. Davidson, Dana Silverbush, Roded Sharan
2011 Lecture Notes in Computer Science
When the input 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

Michael Elberfeld, Danny Segev, Colin R. Davidson, Dana Silverbush, Roded Sharan
2013 Theoretical Computer Science
When the input 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]

Iftah Gamzu, Moti Medina
2012 arXiv   pre-print
This property enables us to modify the best known 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]

Marek Cygan, Guy Kortsarz, Zeev Nutov
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

Marek Cygan, Guy Kortsarz, Zeev Nutov
2013 SIAM Journal on Discrete Mathematics
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 [chapter]

Marek Cygan, Guy Kortsarz, Zeev Nutov
2012 Lecture Notes in Computer Science
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  ...

### Improved Orientations of Physical Networks [chapter]

Iftah Gamzu, Danny Segev, Roded Sharan
2010 Lecture Notes in Computer Science
We develop an 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]

Jean-François Culus, Marc Demange
2006 Lecture Notes in Computer Science
Finally, we investigate the 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]

Mehdy Roayaei, MohammadReza Razzazi
2017 arXiv   pre-print
In the 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

Quanquan C. Liu, Jessica Shi, Shangdi Yu, Laxman Dhulipala, Julian Shun
2022 Proceedings of the 34th ACM Symposium on Parallelism in Algorithms and Architectures
As a by-product, our 𝑘-core decomposition 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.  ...

### A GRASP heuristic for the mixed Chinese postman problem

A Corberán, R Martı́, J.M Sanchis
2002 European Journal of Operational Research
In this paper, we present a heuristic 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

M. Mihail, P. Winkler
1996 Algorithmica
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.  ...  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]

Dana Silverbush, Michael Elberfeld, Roded Sharan
2011 Lecture Notes in Computer Science
In a network 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

Dana Silverbush, Michael Elberfeld, Roded Sharan
2011 Journal of Computational Biology
In a network 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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