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Constant Congestion Routing of Symmetric Demands in Planar Directed Graphs

Chandra Chekuri, Alina Ene, Marcin Pilipczuk
2018 SIAM Journal on Discrete Mathematics  
We study the problem of routing symmetric demand pairs in planar digraphs.  ...  A recent paper by a subset of the authors [7] initiated the study of maximum throughput routing problems in directed graphs where the demand pairs are symmetric.  ...  7:13 Does a planar directed graph with treewidth h have a constant congestion crossbar of size Ω(h). This would strengthen our result. In particular, is there a cylindrical grid minor of size Ω(h)?  ... 
doi:10.1137/17m1150694 fatcat:qzb4xwxhbrctjk6wgsxvnxlrlm

Routing Symmetric Demands in Directed Minor-Free Graphs with Constant Congestion

Timothy Carpenter, Ario Salmasi, Anastasios Sidiropoulos, Michael Wagner
2019 International Workshop on Approximation Algorithms for Combinatorial Optimization  
Recently, [Chekuri, Ene and Pilipczuk 2016] have obtained a polylogarithmic approximation with constant congestion on directed planar graphs, for the special case of symmetric demands.  ...  The problem of routing in graphs using node-disjoint paths has received a lot of attention and a polylogarithmic approximation algorithm with constant congestion is known for undirected graphs [Chuzhoy  ...  The study of maximum throughput routing problems in directed graphs with symmetric demand pairs began in [5] .  ... 
doi:10.4230/lipics.approx-random.2019.14 dblp:conf/approx/CarpenterSS19 fatcat:rcpvl3czyvbxzgilpfnweokr4a

Routing Symmetric Demands in Directed Minor-Free Graphs with Constant Congestion [article]

Timothy Carpenter, Ario Salmasi, Anastasios Sidiropoulos
2017 arXiv   pre-print
Recently, [Chekuri, Ene and Pilipczuk 2016] have obtained a polylogarithmic approximation with constant congestion on directed planar graphs, for the special case of symmetric demands.  ...  The problem of routing in graphs using node-disjoint paths has received a lot of attention and a polylogarithmic approximation algorithm with constant congestion is known for undirected graphs [Chuzhoy  ...  The study of maximum throughput routing problems in directed graphs with symmetric demand pairs began in [5] .  ... 
arXiv:1711.01692v1 fatcat:lnmgosihmjcqbci2ncy2t4lxi4

Oblivious routing on node-capacitated and directed graphs

Mohammad Taghi Hajiaghayi, Robert D. Kleinberg, Harald Räcke, Tom Leighton
2007 ACM Transactions on Algorithms  
For the directed case, however, we show that the lower bound of Ω( √ n) still holds in low-degree graphs.  ...  We show that in fact the degree of a graph is a crucial parameter for node-capacitated oblivious routing in undirected graphs, by providing an O(∆ polylog(n))competitive oblivious routing scheme for graphs  ...  oblivious routing with symmetric demands in edge-capacitated directed graphs is at least Ω( √ n).  ... 
doi:10.1145/1290672.1290688 fatcat:lj7k2xkv65emdeemyswchzzhou

The All-or-Nothing Flow Problem in Directed Graphs with Symmetric Demand Pairs [chapter]

Chandra Chekuri, Alina Ene
2014 Lecture Notes in Computer Science  
We study the approximability of the All-or-Nothing multicommodity flow problem in directed graphs with symmetric demand pairs (SymANF).  ...  We obtain this result by extending the well-linked decomposition framework of [11] to the directed graph setting with symmetric demand pairs.  ...  Our second motivation for studying routing problems in directed graphs with symmetric demand pairs stems from their connections to directed treewidth.  ... 
doi:10.1007/978-3-319-07557-0_19 fatcat:6vl6trtwb5aujbq3m2ctbzneeq

The all-or-nothing flow problem in directed graphs with symmetric demand pairs

Chandra Chekuri, Alina Ene
2014 Mathematical programming  
We study the approximability of the All-or-Nothing multicommodity flow problem in directed graphs with symmetric demand pairs (SymANF).  ...  We obtain this result by extending the well-linked decomposition framework of [11] to the directed graph setting with symmetric demand pairs.  ...  Our second motivation for studying routing problems in directed graphs with symmetric demand pairs stems from their connections to directed treewidth.  ... 
doi:10.1007/s10107-014-0856-z fatcat:l4cjh42tf5evbeprkaikfqwlte

Routing and network design with robustness to changing or uncertain traffic demands

Chandra Chekuri
2007 ACM SIGACT News  
In a different direction, Räcke [52] showed the existence of good randomized oblivious routings in all undirected graphs.  ...  This was followed by a proof of the polynomial time solvability of an optimal oblivious routing scheme [7] . One can view the above developments in a common framework of robust optimization.  ...  Acknowledgments: The author is grateful to his collaborators on [18] for teaching him much of what he knows about this topic.  ... 
doi:10.1145/1324215.1324236 fatcat:urzyd3gbffaexjiscl7pqtqfia

Flow-Cut Gaps for Integer and Fractional Multiflows [chapter]

Chandra Chekuri, F. Bruce Shepherd, Christophe Weibel
2010 Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms  
Consider a routing problem instance consisting of a demand graph H = (V, E(H)) and a supply graph G = (V, E(G)).  ...  A demand is compliant if its endpoints are joined by a directed path in the resulting oriented graph.  ...  We thank an anonymous reviewer for pointing out a minor error in an earlier proof of Theorem 4.9.  ... 
doi:10.1137/1.9781611973075.96 dblp:conf/soda/ChekuriSW10 fatcat:3l2e5rhqenc6jfrnioiv4ealcq

A Note on Multiflows and Treewidth

Chandra Chekuri, Sanjeev Khanna, F. Bruce Shepherd
2007 Algorithmica  
An instance of the problem consists of a capacitated graph and a collection of terminal pairs. Each terminal pair has a non-negative demand that is to be routed between the nodes in the pair.  ...  A class of optimization problems is obtained when the goal is to route a maximum number of the pairs in the graph subject to the capacity constraints on the edges.  ...  EDP was recently shown to be approximable to within O(log n) in planar graphs if congestion of 2 is allowed [10] , and to within a constant if congestion 4 is allowed [13] .  ... 
doi:10.1007/s00453-007-9129-z fatcat:addxk77fejhatpd3v5vufqfy24

Flow-cut gaps for integer and fractional multiflows

Chandra Chekuri, F. Bruce Shepherd, Christophe Weibel
2013 Journal of combinatorial theory. Series B (Print)  
Consider a routing problem instance consisting of a demand graph H = (V, E(H)) and a supply graph G = (V, E(G)).  ...  A demand is compliant if its endpoints are joined by a directed path in the resulting oriented graph.  ...  We thank an anonymous reviewer for pointing out a minor error in an earlier proof of Theorem 4.9.  ... 
doi:10.1016/j.jctb.2012.11.002 fatcat:6g3adrwfajfmfe6qpjqawgyara

Flow-Cut Gaps for Integer and Fractional Multiflows [article]

Chandra Chekuri, F. Bruce Shepherd, Christophe Weibel
2010 arXiv   pre-print
Consider a routing problem consisting of a demand graph H and a supply graph G.  ...  A demand is compliant if its endpoints are joined by a directed path in the resulting oriented graph.  ...  We thank an anonymous reviewer for pointing out a minor error in an earlier proof of Theorem 4.9.  ... 
arXiv:1008.2136v1 fatcat:zrczubo7lfho7jxyfoql5macbe

Lower bounds for graph embeddings and combinatorial preconditioners

Gary L. Miller, Peter C. Richter
2004 Proceedings of the sixteenth annual ACM symposium on Parallelism in algorithms and architectures - SPAA '04  
One example is the routing time ρ(G, H) ≤ O(congestion + dilation), the number of steps necessary to route pairwise demands G on network links H in the store-and-forward packet routing model.  ...  In this paper, we seek to identify the class of graphs G which are intrinsically difficult to approximate by a particular measure.  ...  One such measure is the routing time ρ(G, H) ≤ O(congestion + dilation), the number of steps necessary to route pairwise demands G on network links H in the store-and-forward packet routing model.  ... 
doi:10.1145/1007912.1007929 dblp:conf/spaa/MillerR04 fatcat:2kjzdyqwwvcprhdkiijuan7ppi

On the Approximability of Robust Network Design [article]

Yacine Al-Najjar, and Walid Ben-Ameur, Jeremie Leguay
2021 arXiv   pre-print
We first prove that the robust network design problem with minimum congestion cannot be approximated within any constant factor.  ...  Given the dynamic nature of traffic, we investigate the variant of robust network design where we have to determine the capacity to reserve on each link so that each demand vector belonging to a polyhedral  ...  Notice that the bound given by static routing cannot provide a better bound than O(log n) since a lower bound of Ω(log n) is achieved by static routing for planar graphs [36, 37] .  ... 
arXiv:2009.12291v3 fatcat:js4qvptq3zhmrgdjfouym4o2sa

Vertex Sparsifiers: New Results from Old Techniques

Matthias Englert, Anupam Gupta, Robert Krauthgamer, Harald Räcke, Inbal Talgam-Cohen, Kunal Talwar
2014 SIAM journal on computing (Print)  
congestion up to a constant factor.  ...  k), where k = |K|, (b) a convex combination of trees over the terminals K that maintains congestion up to a factor of O( k), and (c) for a planar graph G, a convex combination of planar graphs that maintains  ...  The same demand can be routed with congestion at most (c + 1) √ log n in G, for some constant c depending on the edge expansion of G. Say each terminal i sends a total flow of 1.  ... 
doi:10.1137/130908440 fatcat:p5ykt26u2fhvzb3ryge6llj6pm

Curvature of Indoor Sensor Network: Clustering Coefficient

F Ariaei, M Lou, E Jonckheere, B Krishnamachari, M Zuniga
2008 EURASIP Journal on Wireless Communications and Networking  
Recommended by Sayandev Mukherjee We investigate the geometric properties of the communication graph in realistic low-power wireless networks.  ...  In particular, we explore the concept of the curvature of a wireless network via the clustering coefficient.  ...  Last but not least, greedy geographic routing on hyperbolic plane embedding of the graph [34] should have better properties (e.g., smaller stretch and congestion) when applied to a graph that is negatively  ... 
doi:10.1155/2008/213185 fatcat:4wpqw6otufeippmamfhwu2b4mu
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