Art gallery theorems and algorithms
Art gallery theorems and algorithms
Introduction to algorithms
Approximation algorithms for scheduling unrelated parallel machines
Mathematical Programming: Series A and B
Planar orientations with low out-degree and compaction of adjacency matrices
Theoretical Computer Science
A faster deterministic maximum flow algorithm
SODA selected papers from the third annual ACM-SIAM symposium on Discrete algorithms
Beyond the flow decomposition barrier
Journal of the ACM (JACM)
Exact and Approximate Algorithms for Scheduling Nonidentical Processors
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Dynamic Representation of Sparse Graphs
WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
Discrete Applied Mathematics
Complexity of approximating the oriented diameter of chordal graphs
Journal of Graph Theory
Balanced vertex-orderings of graphs
Discrete Applied Mathematics
On the complexity of the balanced vertex ordering problem
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Approximation scheme for lowest outdegree orientation and graph density measures
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Graph orientations optimizing the number of light or heavy vertices
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
The 2-valued case of makespan minimization with assignment constraints
Information Processing Letters
Upper and lower degree bounded graph orientation with minimum penalty
CATS '12 Proceedings of the Eighteenth Computing: The Australasian Theory Symposium - Volume 128
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Given a simple, undirected graph G=(V,E) and a weight function w:E驴驴+, we consider the problem of orienting all edges in E so that the maximum weighted outdegree among all vertices is minimized. It has previously been shown that the unweighted version of the problem is solvable in polynomial time while the weighted version is (weakly) NP-hard. In this paper, we strengthen these results as follows: (1) We prove that the weighted version is strongly NP-hard even if all edge weights belong to the set {1,k}, where k is any fixed integer greater than or equal to 2, and that there exists no pseudo-polynomial time approximation algorithm for this problem whose approximation ratio is smaller than (1+1/k) unless P驴=驴NP; (2) we present a new polynomial-time algorithm that approximates the general version of the problem within a ratio of (2驴1/k), where k is the maximum weight of an edge in G; (3) we show how to approximate the special case in which all edge weights belong to {1,k} within a ratio of 3/2 for k=2 (note that this matches the inapproximability bound above), and (2驴2/(k+1)) for any k驴3, respectively, in polynomial time.