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Dense Steiner problems: Approximation algorithms and inapproximability
[article]

2020
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arXiv
*
pre-print

We study a generalization of pairwise δ-dense

arXiv:2004.14102v1
fatcat:25a6a2tufjgulh7qr6dedy3rry
*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. ...##
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A Graph Reduction Step Preserving Element-Connectivity and Applications
[article]

2009
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arXiv
*
pre-print

Our proofs are constructive, giving poly-time algorithms to find these

arXiv:0902.2795v1
fatcat:6t43enzedffzde5bqicnju3dfy
*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. ...##
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A Graph Reduction Step Preserving Element-Connectivity and Applications
[chapter]

2009
*
Lecture Notes in Computer Science
*

Our proofs are constructive, giving poly-time algorithms to find these

doi:10.1007/978-3-642-02927-1_22
fatcat:myvwnoii2jfibd4au4datgdfv4
*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. ...##
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A primal-dual approximation algorithm for the Steiner forest problem

1994
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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-

doi:10.1016/0020-0190(94)00034-4
fatcat:myfqzonuevgwthvaoaheagf5wu
*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*. ...##
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Online Directed Spanners and Steiner Forests
[article]

2021
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arXiv
*
pre-print

We present online algorithms for directed spanners and

arXiv:2103.04543v2
fatcat:r54ordqp7vc37f6kmsrhfvzjqe
*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. ...##
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Page 6627 of Mathematical Reviews Vol. , Issue 92m
[page]

1992
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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. ...##
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Approximate Integer Decompositions for Undirected Network Design Problems

2009
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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

doi:10.1137/040617339
fatcat:xozh3u3w7ngpvfakmhbrwfuwkq
*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. ...##
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Greedy Algorithms for Online Survivable Network Design

2018
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International Colloquium on Automata, Languages and Programming
*

The coefficients of this linear combination are achieved from an

doi:10.4230/lipics.icalp.2018.152
dblp:conf/icalp/DehghaniEHLS18
fatcat:iig474zqjzdcbp3aixsze6fwqu
*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. ...##
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Fast and Deterministic Approximations for k-Cut
[article]

2018
*
arXiv
*
pre-print

The cost of the

arXiv:1807.07143v2
fatcat:nytbhcjjlvgtnb4s4bmqgeaaxi
*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. ...##
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Fast and Deterministic Approximations for k-Cut

2019
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International Workshop on Approximation Algorithms for Combinatorial Optimization
*

Each Lagrangian relaxation is designed to steer y away from

doi:10.4230/lipics.approx-random.2019.23
dblp:conf/approx/Quanrud19
fatcat:ffcftkfmlrhypb3bxm7oggfthy
*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. ...##
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Online Weighted Degree-Bounded Steiner Networks via Novel Online Mixed Packing/Covering
[article]

2017
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arXiv
*
pre-print

We design the first online algorithm with poly-logarithmic competitive ratio for the edge-weighted degree-bounded

arXiv:1704.05811v1
fatcat:nferpbdlxvhtvhnmitx62ix7ji
*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*. ...##
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Page 1946 of Mathematical Reviews Vol. , Issue 95d
[page]

1995
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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. ...##
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Thrifty Algorithms for Multistage Robust Optimization
[article]

2013
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arXiv
*
pre-print

We show similar thrifty algorithms for multi-stage k-robust

arXiv:1302.5445v1
fatcat:6hthjvme6rcllfnar27otgpfqa
*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. ...##
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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*. ...##
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Improved Approximation Algorithms for PRIZE-COLLECTING STEINER TREE and TSP

2009
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2009 50th Annual IEEE Symposium on Foundations of Computer Science
*

We study the prize-collecting versions of the

doi:10.1109/focs.2009.39
dblp:conf/focs/ArcherBHK09
fatcat:had4l3yaabbzdguvvzdaiq4f5a
*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. ...
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