Kiyohito NAGANO\dagger (11Lnnnnn!!!llll)))BggX) Abstract A linearly parameterized polymatroid intersection problem appears in the context of principal partitions. We consider a submodular intersection problem on a pair of strong-map sequences of submodular functions, which is an extension of the linearly parameterized polymatroid intersection problem to a nonlinearly parameterized one. We intro...

Unit disk graphs are intersection graphs of circles of unit radius in the plane. We present simple and provably good heuristics for a number of classical NP-hard optimization problems on unit disk graphs. The problems considered include maximum independent set, minimum vertex cover, minimum coloring and minimum dominating set. We also present an on-line coloring heuristic which achieves a compe...

In this paper, we give method for probabilistic assignment to the Realistic Abduc-tive Reasoning Model, proposed in 1]. The knowledge is assumed to be represented in the form of causal chaining, namely, hyper-bipartite network. Hyper-bipartite network is the most generalized form of knowledge representation for which, so far, there has been no way of assigning the probability to the explanation...

Knowledge representation is a popular research field in IT. As mathematical knowledge is most formalized, its representation is important and interesting. Mathematical knowledge consists of various mathematical theories. In this paper we consider a deductive system that derives mathematical notions, axioms and theorems. All these notions, axioms and theorems can be considered a small mathematic...

Unit disk graphs are intersection graphs of circles of unit radius in the plane. We present simple and provably good heuristics for a number of classical NP-hard optimization problems on unit disk graphs. The problems considered include maximum independent set, minimum vertex cover, minimum coloring and minimum dominating set. We also present an on-line coloring heuristic which achieves a compe...

A set S of vertices in a graph G=(V,E) is a dominating set ofG if every vertex of V-S is adjacent to some vertex of S.For an integer k≥1, a set S of vertices is a k-step dominating set if any vertex of $G$ is at distance k from somevertex of S. In this paper, using membership values of vertices and edges in fuzzy graphs, we introduce the concepts of strength of strongestdominating set as well a...

Finding a dominating set of minimum cardinality is an NP-hard graph problem, even when the graph is bipartite. In this paper we are interested in solving the problem on graphs having a large independent set. Given a graph G with an independent set of size z, we show that the problem can be solved in time O∗(2n−z), where n is the number of vertices of G. As a consequence, our algorithm is able t...

A stable set in a graph G is a set of mutually non-adjacent vertices, α(G) is the size of a maximum stable set of G, and core(G) is the intersection of all its maximum stable sets. In this paper we demonstrate that in a tree T , of order n ≥ 2, any stable set of size ≥ n/2 contains at least one pendant vertex. Hence, we deduce that any maximum stable set in a tree contains at least one pendant ...

A unit disk graph is the intersection graph of unit disks in the euclidean plane. We present a polynomial-time approximation scheme for the maximum weight independent set problem in unit disk graphs. In contrast to previously known approximation schemes, our approach does not require a geometric representation (specifying the coordinates of the disk centers). The approximation algorithm present...