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Dense Steiner problems: Approximation algorithms and inapproximability [article]

Marek Karpinski, Mateusz Lewandowski, Syed Mohammad Meesum, Matthias Mnich
2020 arXiv   pre-print
We study a generalization of pairwise δ-dense Steiner Forest, which asks for a minimum-size forest in G in which the nodes in each terminal set T_1,...  ...  We also consider the δ-dense Group Steiner Tree problem as defined by Hauptmann and show that the problem is APX-hard.  ...  Our results show a connection between dense instances of Steiner Forest and Set Packing problem.  ... 
arXiv:2004.14102v1 fatcat:25a6a2tufjgulh7qr6dedy3rry

A Graph Reduction Step Preserving Element-Connectivity and Applications [article]

Chandra Chekuri, Nitish Korula
2009 arXiv   pre-print
Our proofs are constructive, giving poly-time algorithms to find these forests; these are the first non-trivial algorithms for packing element-disjoint Steiner Forests. 2.  ...  ., T_m, we seek a maximum number of element-disjoint Steiner forests where each forest connects each T_i.  ...  We thank Joseph Cheriyan for asking about planar packing of Steiner Trees which inspired our work on that problem.  ... 
arXiv:0902.2795v1 fatcat:6t43enzedffzde5bqicnju3dfy

A Graph Reduction Step Preserving Element-Connectivity and Applications [chapter]

Chandra Chekuri, Nitish Korula
2009 Lecture Notes in Computer Science  
Our proofs are constructive, giving poly-time algorithms to find these forests; these are the first non-trivial algorithms for packing element-disjoint Steiner Forests. • We give a very short and intuitive  ...  . , T m , we seek a maximum number of elementdisjoint Steiner forests where each forest connects each T i .  ...  We thank Joseph Cheriyan for asking about planar packing of Steiner Trees which inspired our work on that problem.  ... 
doi:10.1007/978-3-642-02927-1_22 fatcat:myvwnoii2jfibd4au4datgdfv4

A primal-dual approximation algorithm for the Steiner forest problem

R. Ravi
1994 Information Processing Letters  
Given an undirected graph with nonnegative edge-costs, a subset of nodes of size k called the terminals, and an integer q between 1 and k, the minimum q-Steiner forest problem is to find a forest of minimum  ...  When q = 1, we have the classical minimum-cost Steiner tree problem on networks.  ...  Our algorithm is primal-dual in that it runs in iterations and, in each iteration, collects a greedy c-packing of multicuts and at the same time partially constructs the Steiner forest.  ... 
doi:10.1016/0020-0190(94)00034-4 fatcat:myfqzonuevgwthvaoaheagf5wu

Online Directed Spanners and Steiner Forests [article]

Elena Grigorescu, Young-San Lin, Kent Quanrud
2021 arXiv   pre-print
We present online algorithms for directed spanners and Steiner forests.  ...  We convert the online spanner problem and the online Steiner forest problem into online covering problems and round in a problem-specific fashion.  ...  Steiner forest problem.  ... 
arXiv:2103.04543v2 fatcat:r54ordqp7vc37f6kmsrhfvzjqe

Page 6627 of Mathematical Reviews Vol. , Issue 92m [page]

1992 Mathematical Reviews  
K. (1-BELL) A proof of the Gilbert-Pollak conjecture on the Steiner ratio. The Steiner problem. Algorithmica 7 (1992), no. 2-3, 121-135.  ...  A forest F in H will be said to be end-faithful if, for each end éy in H, there exists exactly one end é¢- in F such that er C en.  ... 

Approximate Integer Decompositions for Undirected Network Design Problems

Chandra Chekuri, F. Bruce Shepherd
2009 SIAM Journal on Discrete Mathematics  
We show that the splitting-off theorem of Mader in undirected graphs implies a generalization of this to finding k edgedisjoint Steiner forests in Eulerian graphs.  ...  This leads to new 2-approximation rounding algorithms for constrained 0-1 forest problems considered by Goemans and Williamson.  ...  Packing Steiner Forests. In this section we prove Lemma 1.3.  ... 
doi:10.1137/040617339 fatcat:xozh3u3w7ngpvfakmhbrwfuwkq

Greedy Algorithms for Online Survivable Network Design

Sina Dehghani, Soheil Ehsani, MohammadTaghi Hajiaghayi, Vahid Liaghat, Saeed Seddighin, Michael Wagner
2018 International Colloquium on Automata, Languages and Programming  
The coefficients of this linear combination are achieved from an Steiner forest packing of the optimum solution.  ...  In the fractional Steiner forest packing problem, the output is a fractional assignment x over T such that for every edge e, T ∈T :e∈T x T is not more than one.  ... 
doi:10.4230/lipics.icalp.2018.152 dblp:conf/icalp/DehghaniEHLS18 fatcat:iig474zqjzdcbp3aixsze6fwqu

Fast and Deterministic Approximations for k-Cut [article]

Kent Quanrud
2018 arXiv   pre-print
The cost of the Steiner cut packing is within a (1) )-multiplicative factor of the corresponding Steiner tree.  ...  For the minimum weight Steiner tree problem, the primal-dual framework returns a Steiner tree and a feasible fractional cut packing in the dual LP.  ... 
arXiv:1807.07143v2 fatcat:nytbhcjjlvgtnb4s4bmqgeaaxi

Fast and Deterministic Approximations for k-Cut

Kent Quanrud, Michael Wagner
2019 International Workshop on Approximation Algorithms for Combinatorial Optimization  
Each Lagrangian relaxation is designed to steer y away from packing forests that have edges that are already tightly packed.  ...  The dual of (C) is the LP (P), which packs forests in the graph and weights each forest by the number of edges minus (n − k).  ...  The cost of the Steiner cut packing is within a 2(1 − o( 1 ))-multiplicative factor of the corresponding Steiner tree.  ... 
doi:10.4230/lipics.approx-random.2019.23 dblp:conf/approx/Quanrud19 fatcat:ffcftkfmlrhypb3bxm7oggfthy

Online Weighted Degree-Bounded Steiner Networks via Novel Online Mixed Packing/Covering [article]

Sina Dehghani, Soheil Ehsani, MohammadTaghi Hajiaghayi, Vahid Liaghat, Harald Racke, Saeed Seddighin
2017 arXiv   pre-print
We design the first online algorithm with poly-logarithmic competitive ratio for the edge-weighted degree-bounded Steiner forest(EW-DB-SF) problem and its generalized variant.  ...  In the offline setting edge-weighted degree-bounded Steiner tree (EW-DB-ST) and its many variations have been extensively studied since early eighties.  ...  The following integer program is a natural mixed packing and covering integer program for ONLINE EDGE-WEIGHTED DEGREE-BOUNDED STEINER FOREST.  ... 
arXiv:1704.05811v1 fatcat:nferpbdlxvhtvhnmitx62ix7ji

Page 1946 of Mathematical Reviews Vol. , Issue 95d [page]

1995 Mathematical Reviews  
If the forests are sampled from #(n,N) with uniform distribution, let 7 be the random variable equal to the height of a forest from #(n, N).  ...  This paper contains an interesting theorem on full Steiner trees.  ... 

Thrifty Algorithms for Multistage Robust Optimization [article]

Anupam Gupta and Viswanath Nagarajan and Vijay V. Vazirani
2013 arXiv   pre-print
We show similar thrifty algorithms for multi-stage k-robust Steiner tree, Steiner forest, and minimum-cut.  ...  Proof: Consider the dual of the Steiner forest LP relaxation, which is a packing problem.  ...  Robust versions of Steiner tree/forest, minimum cut, and other covering problems are similarly defined.  ... 
arXiv:1302.5445v1 fatcat:6hthjvme6rcllfnar27otgpfqa

Page 45 of Mathematical Reviews Vol. , Issue 2000a [page]

2000 Mathematical Reviews  
Similarly, the case v = 4 (mod 6) for 2000a:05064 Kirkman packing designs can be done using standard techniques. The remaining case for Kirkman packings, v = | (mod 6), re- quires a bit more work.  ...  (RS-AOS-SY; Moscow) Locally explicit construction of Rédl’s asymptotically good packings.  ... 

Improved Approximation Algorithms for PRIZE-COLLECTING STEINER TREE and TSP

Aaron Archer, Mohammad Hossein Bateni, Mohammad Taghi Hajiaghayi, Howard Karloff
2009 2009 50th Annual IEEE Symposium on Foundations of Computer Science  
We study the prize-collecting versions of the Steiner tree, traveling salesman, and stroll (a.k.a.  ...  Because of this rule, F remains a forest.  ...  Suppose a vector y of dual variables obeys all of the edge packing constraints of LP (3), but not necessarily the penalty packing constraints.  ... 
doi:10.1109/focs.2009.39 dblp:conf/focs/ArcherBHK09 fatcat:had4l3yaabbzdguvvzdaiq4f5a
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