A fast parametric maximum flow algorithm and applications
SIAM Journal on Computing
On cutting a few vertices from a graph
Discrete Applied Mathematics
Bi-criteria algorithm for scheduling jobs on cluster platforms
Proceedings of the sixteenth annual ACM symposium on Parallelism in algorithms and architectures
Approximation algorithms for the bi-criteria weighted MAX-CUT problem
Discrete Applied Mathematics
Approximation algorithms for maximum cut with limited unbalance
Theoretical Computer Science
Submodular Approximation: Sampling-based Algorithms and Lower Bounds
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
An annotated bibliography of combinatorial optimization problems with fixed cardinality constraints
Discrete Applied Mathematics - Special issue: 2nd cologne/twente workshop on graphs and combinatorial optimization (CTW 2003)
ESA'05 Proceedings of the 13th annual European conference on Algorithms
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We present the Minimum Cut with Bounded Size problem and two efficient algorithms for its solution. In this problem we want to partition the n vertices of a edge-weighted graph into two sets S and T, with S including a given source s, T a given sink t, and with |S| bounded by a given threshold B, so as to minimize the weight δ (S) of the edges crossing the cut (S,T). If B is equal to n-1 the problem is well-known to be solvable in polynomial time, but for general B it becomes NP-hard. The first algorithm is randomized and, for each ε 0, it returns, with high probability, a solution S having a weight within ratio (1+ εB/logn) of the optimum. The second algorithm is a deterministic bicriteria algorithm which can return a solution violating the cardinality constraint within a specified ratio; precisely, for each 0 S having either (1) a weight within ratio 1/1-γ of the optimum or (2) optimum weight but cardinality |S|≤ = B/γ, and hence it violates the constraint by a factor at most 1/γ.