TY - GEN

T1 - Network-design with degree constraints

AU - Khandekar, Rohit

AU - Kortsarz, Guy

AU - Nutov, Zeev

PY - 2011

Y1 - 2011

N2 - We study several network design problems with degree constraints. For the degree-constrained 2-connected subgraph problem we obtain a factor 6 violation for the degrees with 4 approximation for the cost. This improves upon the logarithmic degree violation and no cost guarantee obtained by Feder, Motwani, and Zhu (2006). Then we consider the problem of finding an arborescence with at least k terminals and with minimum maximum outdegree. We show that the natural LP-relaxation has a gap of Ω (√k) or Ω (n1/4) with respect to the multiplicative degree bound violation. We overcome this hurdle by a combinatorial O(√(k log k)/Δ*)-approximation algorithm, where Δ* denotes the maximum degree in the optimum solution. We also give an Ω(log n) lower bound on approximating this problem. Then we consider the undirected version of this problem, however, with an extra diameter constraint, and give an Ω(log n) lower bound on the approximability of this version. Finally, we consider a closely related prize-collecting degree-constrained Steiner Network problem. We obtain several results in this direction by reducing the prize-collecting variant to the regular one.

AB - We study several network design problems with degree constraints. For the degree-constrained 2-connected subgraph problem we obtain a factor 6 violation for the degrees with 4 approximation for the cost. This improves upon the logarithmic degree violation and no cost guarantee obtained by Feder, Motwani, and Zhu (2006). Then we consider the problem of finding an arborescence with at least k terminals and with minimum maximum outdegree. We show that the natural LP-relaxation has a gap of Ω (√k) or Ω (n1/4) with respect to the multiplicative degree bound violation. We overcome this hurdle by a combinatorial O(√(k log k)/Δ*)-approximation algorithm, where Δ* denotes the maximum degree in the optimum solution. We also give an Ω(log n) lower bound on approximating this problem. Then we consider the undirected version of this problem, however, with an extra diameter constraint, and give an Ω(log n) lower bound on the approximability of this version. Finally, we consider a closely related prize-collecting degree-constrained Steiner Network problem. We obtain several results in this direction by reducing the prize-collecting variant to the regular one.

UR - http://www.scopus.com/inward/record.url?scp=80052357697&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-22935-0_25

DO - 10.1007/978-3-642-22935-0_25

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AN - SCOPUS:80052357697

SN - 9783642229343

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 289

EP - 301

BT - Approximation, Randomization, and Combinatorial Optimization

T2 - 14th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2011 and the 15th International Workshop on Randomization and Computation, RANDOM 2011

Y2 - 17 August 2011 through 19 August 2011

ER -