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Search results for: computational complexity
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Domination subdivision and domination multisubdivision numbers of graphs
PublicationThe domination subdivision number sd(G) of a graph G is the minimum number of edges that must be subdivided (where an edge can be subdivided at most once) in order to increase the domination number of G. It has been shown [10] that sd(T)<=3 for any tree T. We prove that the decision problem of the domination subdivision number is NP-complete even for bipartite graphs. For this reason we define the domination multisubdivision number...
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Polynomial Algorithm for Minimal (1,2)-Dominating Set in Networks
PublicationDominating sets find application in a variety of networks. A subset of nodes D is a (1,2)-dominating set in a graph G=(V,E) if every node not in D is adjacent to a node in D and is also at most a distance of 2 to another node from D. In networks, (1,2)-dominating sets have a higher fault tolerance and provide a higher reliability of services in case of failure. However, finding such the smallest set is NP-hard. In this paper, we...
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Weighted 2-sections and hypergraph reconstruction
PublicationIn the paper we introduce the notion of weighted 2-sections of hypergraphs with integer weights and study the following hypergraph reconstruction problems: (1) Given a weighted graph , is there a hypergraph H such that is its weighted 2-section? (2) Given a weighted 2-section , find a hypergraph H such that is its weighted 2-section. We show that (1) is NP-hard even if G is a complete graph or integer weights w does not exceed...
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Paired domination subdivision and multisubdivision numbers of graphs
PublicationThe paired domination subdivision number sdpr(G) of a graph G is the minimum number of edges that must be subdivided (where an edge can be subdivided at most once) in order to increase the paired domination number of G. We prove that the decision problem of the paired domination subdivision number is NP-complete even for bipartite graphs. For this reason we define the paired domination muttisubdivision number of a nonempty graph...
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Collaborative Delivery by Energy-Sharing Low-Power Mobile Robots
PublicationWe study two variants of delivery problems for mobile robots sharing energy. Each mobile robot can store at any given moment at most two units of energy, and whenever two robots are at the same location, they can transfer energy between each other, respecting the maximum capacity. The robots operate in a simple graph and initially each robot has two units of energy. A single edge traversal by an robot reduces its energy by one...
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On Computational Aspects of Greedy Partitioning of Graphs
PublicationIn this paper we consider a problem of graph P-coloring consisting in partitioning the vertex set of a graph such that each of the resulting sets induces a graph in a given additive, hereditary class of graphs P. We focus on partitions generated by the greedy algorithm. In particular, we show that given a graph G and an integer k deciding if the greedy algorithm outputs a P-coloring with a least k colors is NP-complete for an infinite...
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On the hardness of computing span of subcubic graphs
PublicationIn the paper we study the problem of finding ξ-colorings with minimal span, i.e. the difference between the largest and the smallest color used.
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Quantum-classical calculations of the nanomechanical properties of metals
PublicationTradycyjnie symulacje komputerowe układów w skali atomowej prowadzone są przy użyciu klasycznej metody dynamiki molekularnej (MD) bądź kwantowych metod ab initio. Główną wadą ujęcia klasycznego jest jego empiryczna natura, a co za tym idzie - niewielka przenośność, jego prostota natomiast pozwala na przeprowadzanie symulacji układów zawierających miliony atomów. W wyniku zastosowania metod kwantowych otrzymuje się bardziej wiarygodne...
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The Role of Daylight in Forming the Traditional Space: Classification of Traditional Iranian Daylighting Elements
PublicationDaylight character in a space can be defined as the manner in which daylight permeates and is dispersed in that space. The architectural elements related to daylighting under investigation in this study were rooted in Iranian-Isfahani heritage, considered traditional Iranian architecture (from the 16th to early 20th century). The establishment of a classification system for daylighting systems holds significant utility. This...