Exact Max-SAT solvers, compared with SAT solvers, apply little inference at each node of the proof tree. Commonly used SAT inference rules like unit propagation produce a simplified formula that preserves satisfiability but, unfortunately, solving the Max-SAT problem for the simplified formula is not equivalent to solving it for the original formula. In this paper, we define a number of origina...

The max-k-cut problem is to partition the vertices of a weighted graph G = (V, E) into k ≥ 2 disjoint subsets such that the weight sum of the edges crossing the different subsets is maximized. The problem is referred as the max-cut problem when k = 2. In this work, we present a multiple operator heuristic (MOH) for the general max-k-cut problem. MOH employs five distinct search operators organi...

In this paper we study output coding for multi-label prediction. For a multi-label output coding to be discriminative, it is important that codewords for different label vectors are significantly different from each other. In the meantime, unlike in traditional coding theory, codewords in output coding are to be predicted from the input, so it is also critical to have a predictable label encodi...

We prove upper and lower bounds on performance guarantees of approximation algorithms for the Hierarchical MAX-SAT (H-MAX-SAT) problem. This problem is representative of a broad class of PSPACE-hard problems involving graphs, Boolean formulas and other structures that are de ned succinctly. Our rst result is that for some constant < 1, it is PSPACE-hard to approximate the function H-MAX-SAT to ...

Given a graph G=(V, E), a connected sides cut (U, V\U) or δ(U) is the set of edges of E linking all vertices of U to all vertices of V\U such that the induced subgraphs G[U] and G[V\U] are connected. Given a positive weight function w defined on E, the maximum connected sides cut problem is to find a connected sides cut Ω such that w(Ω) is maximum. This problem is NP-hard. In this paper, we giv...

As an example, we note that the bipartite graph has maxcut exactly equal to the sum of the weights of all its edges. A particular case of the MAX-CUT problem occurs when all the edge weights are reduced to unity. In that case it becomes equivalent to the MAX-2COLORING problem. In the MAX-2COLORING problem, we try to find the maximum number of edges in a given graph G which can be colored by usi...

We study the problem k-Set Splitting in fixed parameter complexity. We show that the problem can be solved in time O∗(2.6494k), improving on the best currently known running time of O∗(8k). This is done by showing that a non-trivial instance must have a small minimal Set Cover, and using this to reduce the problem to a series of small instances of Max Sat. We also give a linear kernel containin...