The LM-Cut planner uses the landmark-cut heuristic, introduced by the authors in 2009, within a standard A∗ progression search framework to find optimal sequential plans for STRIPS-style planning tasks. This short paper recapitulates the main ideas surrounding the landmark-cut heuristic and provides pointers for further reading.

Partitioning of a graph representation, defined over low-level image features based on Gestalt inspired relations, is an effective strategy for forming coherent perceptual groups in an image. The usual practice, mainly motivated by efficiency considerations, is to approximate the general K-way partitioning solution by recursive bi-partitioning, where at each step the graph is broken into two pa...

Branch-and-cut methods are exact algorithms for integer programming problems. They consist of a combination of a cutting plane method with a branch-and-bound algorithm. These methods work by solving a sequence of linear programming relaxations of the integer programming problem. Cutting plane methods improve the relaxation of the problem to more closely approximate the integer programming probl...

An odd hole is an induced odd cycle of length at least 5. Scott and Seymour confirmed a conjecture of Gyárfás and proved that if a graph G has no odd holes then χ(G) 6 22 ω(G)+2 . Chudnovsky, Robertson, Seymour and Thomas showed that if G has neither K4 nor odd holes then χ(G) 6 4. In this note, we show that if a graph G has neither triangles nor quadrilaterals, and has no odd holes of length a...

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.

The cut number S(d) of the d-cube is the minimum number of hyperplanes in R that slice, that is cut the edges while avoiding vertices, all the edges of the d-cube. The cut number problem for the hypercube of dimensions d ≥ 4 was posed by P. O’Neil more than thirty years ago [17]. The identity S(3) = 3 is easy and that of S(4) = 4 is a well-known result, see [5,6,18]. However, the conjecture of ...

Let an edge cut partition the vertex set of the n-cube into k subsets A1, ..., Ak with ||Ai| − |Aj || ≤ 1. We consider the problem to determine minimal size of such a cut and present its asymptotic as n, k → ∞ and also as n → ∞ and k is a constant of the form k = 2a ± 2b with a ≥ b ≥ 0.

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...