Novel algorithms for the network lifetime problem in wireless settings
Wireless Networks
Network-design with degree constraints
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Matroidal degree-bounded minimum spanning trees
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Degree-Constrained node-connectivity
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Simpler analysis of LP extreme points for traveling salesman and survivable network design problems
Operations Research Letters
Network design with weighted degree constraints
Discrete Optimization
Improved approximation algorithms for maximum lifetime problems in wireless networks
Theoretical Computer Science
Constrained matching problems in bipartite graphs
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
On some network design problems with degree constraints
Journal of Computer and System Sciences
Chain-Constrained spanning trees
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
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We present polynomial-time approximation algorithms for some degree-bounded directed network design problems. Our main result is for intersecting supermodular connectivity requirements with degree bounds: given a directed graph $G=(V,E)$ with nonnegative edge-costs, a connectivity requirement specified by an intersecting supermodular function $f$, and upper bounds $\{a_v,b_v\}_{v\in V}$ on in-degrees and out-degrees of vertices, find a minimum-cost $f$-connected subgraph of $G$ that satisfies the degree bounds. We give a bicriteria approximation algorithm for this problem using the natural LP relaxation and show that our guarantee is the best possible relative to this LP relaxation. We also obtain similar results for the (more general) class of crossing supermodular requirements. In the absence of edge-costs, our result gives the first additive $O(1)$-approximation guarantee for degree-bounded intersecting/crossing supermodular connectivity problems. We also consider the minimum crossing spanning tree problem: Given an undirected edge-weighted graph $G$, edge-subsets $\{E_i\}_{i=1}^k$, and nonnegative integers $\{b_i\}_{i=1}^k$, find a minimum-cost spanning tree (if it exists) in $G$ that contains at most $b_i$ edges from each set $E_i$. We obtain a $+(r-1)$ additive approximation for this problem, when each edge lies in at most $r$ sets. A special case of this problem is the degree-bounded minimum spanning tree, and our techniques give a substantially shorter proof of the recent $+1$ approximation of Singh and Lau [in Proceedings of the 40th Annual ACM Symposium on Theory of Computing, 2007, pp. 661-670].