In this paper, we provide complete classification of classes of bipartite graphs defined by a single forbidden induced bipartite subgraph with respect to bounded/unbounded clique-width.

We propose a new similarity-based technique for declustering data. The proposed method can adapt to available information about query distributions, data distributions, data sizes and partition-size constraints. The method is based on max-cut partitioning of a similarity graph deened over the given set of data, under constraints on the partition sizes. It maximizes the chances that a pair of da...

We consider the positive semidefinite (psd) matrices with binary entries. We give a characterisation of such matrices, along with a graphical representation. We then move on to consider the associated integer polytopes. Several important and well-known integer polytopes — the cut, boolean quadric, multicut and clique partitioning polytopes — are shown to arise as projections of binary psd polyt...

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We investigate a natural online version of the well-known Maximum Directed Cut problem on DAGs. We propose a deterministic algorithm and show that it achieves a competitive ratio of 3 √ 3

2.1 Greedy algorithm We can think of the cut as a partition of verticesl C = (S, V \ S) whiere S ⊆ V . We can switch between different cuts by moving vertices across the cut, in to or out of S. Moving v across the cut swaps its cut edges with its non-cut edges. This increase the value of the cut when the total weight of its non-cut edges exceeds the weight of the cut edges. If v ∈ S (and simila...

We study the problem of nding the minimum bisection of a graph into two parts of prescribed sizes. We formulate two lower bounds on the problem by relaxing nodeand edgeincidence vectors of cuts. We prove that both relaxations provide the same bound. The main fact we prove is that the duality between the relaxed edgeand nodevectors preserves very natural cardinality constraints on cuts. We prese...

For multilevel-coded modulation, the cut-off rate of multiple antenna systems over frequency-flat, fast fading channels is derived. Following Wozencraft’s approach, a closed-form expression for the cut-off rate is obtained as a function of energy ratio per dimension It is shown that the maximum value of cut-off rate increases linearly with the number of transmit antennas. key words: cut-off rat...

We consider the max-cut problem on a random graph G with n vertices and weights wij being independent bounded random variables with the same xed positive expectation and variance . It is well known that the max-cut number mc(G) always exceeds 2 ∑ i¡j wij . We prove that with probability greater than pn the max-cut number satis es