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    Tytuł:
    NP-completeness of weakly convex and convex dominating set decision problems
    Autorzy:
    Raczek, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/2050778.pdf
    Data publikacji:
    2004
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    dominating set
    NP-completeness
    distance
    convex set
    Opis:
    The convex domination number and the weakly convex domination number are new domination parameters. In this paper we show that the decision problems of convex and weakly convex dominating sets are NP-complete for bipartite and split graphs. Using a modified version of Warshall algorithm we can verify in polynomial time whether a given subset of vertices of a graph is convex or weakly convex.
    Źródło:
    Opuscula Mathematica; 2004, 24, 2; 189-196
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Balanced problems on graphs with categorization of edges
    Autorzy:
    Berežný, Štefan
    Lacko, Vladimír
    Powiązania:
    https://bibliotekanauki.pl/articles/743374.pdf
    Data publikacji:
    2003
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    algorithms on graphs
    categorization of edges
    NP-completeness
    Opis:
    Suppose a graph G = (V,E) with edge weights w(e) and edges partitioned into disjoint categories S₁,...,Sₚ is given. We consider optimization problems on G defined by a family of feasible sets (G) and the following objective function:
    $L₅(D) = max_{1≤i≤p} (max_{e ∈ S_i ∩ D} w(e) - min_{e ∈ S_i ∩ D} w(e))$
    For an arbitrary number of categories we show that the L₅-perfect matching, L₅-a-b path, L₅-spanning tree problems and L₅-Hamilton cycle (on a Halin graph) problem are NP-complete.
    We also summarize polynomiality results concerning above objective functions for arbitrary and for fixed number of categories.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2003, 23, 1; 5-21
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Problems remaining NP-complete for sparse or dense graphs
    Autorzy:
    Schiermeyer, Ingo
    Powiązania:
    https://bibliotekanauki.pl/articles/972006.pdf
    Data publikacji:
    1995
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Computational Complexity
    NP-Completeness
    Hamiltonian Circuit
    Hamiltonian Path
    Independent Set
    Opis:
    For each fixed pair α,c > 0 let INDEPENDENT SET ($m ≤ cn^α$) and INDEPENDENT SET ($m ≥ (ⁿ₂) - cn^α$) be the problem INDEPENDENT SET restricted to graphs on n vertices with $m ≤ cn^α$ or $m ≥ (ⁿ₂) - cn^α$ edges, respectively. Analogously, HAMILTONIAN CIRCUIT ($m ≤ n + cn^α$) and HAMILTONIAN PATH ($m ≤ n + cn^α$) are the problems HAMILTONIAN CIRCUIT and HAMILTONIAN PATH restricted to graphs with $m ≤ n + cn^α$ edges. For each ϵ > 0 let HAMILTONIAN CIRCUIT (m ≥ (1 - ϵ)(ⁿ₂)) and HAMILTONIAN PATH (m ≥ (1 - ϵ)(ⁿ₂)) be the problems HAMILTONIAN CIRCUIT and HAMILTONIAN PATH restricted to graphs with m ≥ (1 - ϵ)(ⁿ₂) edges.
    We prove that these six restricted problems remain NP-complete. Finally, we consider sufficient conditions for a graph to have a Hamiltonian circuit. These conditions are based on degree sums and neighborhood unions of independent vertices, respectively. Lowering the required bounds the problem HAMILTONIAN CIRCUIT jumps from 'easy' to 'NP-complete'.
    Źródło:
    Discussiones Mathematicae Graph Theory; 1995, 15, 1; 33-41
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A Note on Polynomial Algorithm for Cost Coloring of Bipartite Graphs with Δ ≤ 4
    Autorzy:
    Giaro, Krzysztof
    Kubale, Marek
    Powiązania:
    https://bibliotekanauki.pl/articles/31526308.pdf
    Data publikacji:
    2020-08-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    bipartite graph
    chromatic sum
    cost coloring
    NP-completeness
    polynomial algorithm
    Opis:
    In the note we consider vertex coloring of a graph in which each color has an associated cost which is incurred each time the color is assigned to a vertex. The cost of coloring is the sum of costs incurred at each vertex. We show that the minimum cost coloring problem for n-vertex bipartite graph of degree Δ ≤ 4 can be solved in O(n2) time. This extends Jansen’s result [K. Jansen, The optimum cost chromatic partition problem, in: Proc. CIAC’97, Lecture Notes in Comput. Sci. 1203 (1997) 25–36] for paths and cycles to subgraphs of biquartic graphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2020, 40, 3; 885-891
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Efficient list cost coloring of vertices and/or edges of bounded cyclicity graphs
    Autorzy:
    Giaro, Krzysztof
    Kubale, Marek
    Powiązania:
    https://bibliotekanauki.pl/articles/744404.pdf
    Data publikacji:
    2009
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    cost coloring
    dynamic programming
    list coloring
    NP-completeness
    polynomial-time algorithm
    Opis:
    We consider a list cost coloring of vertices and edges in the model of vertex, edge, total and pseudototal coloring of graphs. We use a dynamic programming approach to derive polynomial-time algorithms for solving the above problems for trees. Then we generalize this approach to arbitrary graphs with bounded cyclomatic numbers and to their multicolorings.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2009, 29, 2; 361-376
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the Complexity of the 3-Kernel Problem in Some Classes of Digraphs
    Autorzy:
    Hell, Pavol
    Hernández-Cruz, César
    Powiązania:
    https://bibliotekanauki.pl/articles/30147225.pdf
    Data publikacji:
    2014-02-01
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    kernel
    3-kernel
    NP-completeness
    multipartite tournament
    cyclically 3-partite digraphs
    k-quasi-transitive digraph
    Opis:
    Let D be a digraph with the vertex set V (D) and the arc set A(D). A subset N of V (D) is k-independent if for every pair of vertices u, v ∈ N, we have d(u, v), d(v, u) ≥ k; it is l-absorbent if for every u ∈ V (D) − N there exists v ∈ N such that d(u, v) ≤ l. A k-kernel of D is a k-independent and (k − 1)-absorbent subset of V (D). A 2-kernel is called a kernel. It is known that the problem of determining whether a digraph has a kernel (“the kernel problem”) is NP-complete, even in quite restricted families of digraphs. In this paper we analyze the computational complexity of the corresponding 3-kernel problem, restricted to three natural families of digraphs. As a consequence of one of our main results we prove that the kernel problem remains NP-complete when restricted to 3-colorable digraphs.
    Źródło:
    Discussiones Mathematicae Graph Theory; 2014, 34, 1; 167-185
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A note on hardness of multiprocessor scheduling with scheduling solution space tree
    Autorzy:
    Dwibedy, Debasis
    Mohanty, Rakesh
    Powiązania:
    https://bibliotekanauki.pl/articles/27312879.pdf
    Data publikacji:
    2023
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    combinatorial structures
    computational complexity
    hardness
    makespan
    multiprocessor scheduling
    multiuser
    NP-completeness
    nondeterministic algorithms
    reduction
    scheduling solution space tree
    Opis:
    We study the hardness of the non-preemptive scheduling problem of a list of independent jobs on a set of identical parallel processors with a makespan minimization objective. We make a maiden attempt to explore the combinatorial structure of the problem by introducing a scheduling solution space tree (SSST) as a novel data structure. We formally define and characterize the properties of SSST through our analytical results. We show that the multiprocessor scheduling problem is N P-complete with an alternative technique using SSST and weighted scheduling solution space tree (WSSST) data structures. We propose a non-deterministic polynomial-time algorithm called magic scheduling (MS) based on the reduction framework. We also define a new variant of multiprocessor scheduling by including the user as an additional input parameter, which we called the multiuser multiprocessor scheduling problem (MUMPSP). We also show that MUMPSP is N P-complete. We conclude the article by exploring several non-trivial research challenges for future research investigations.
    Źródło:
    Computer Science; 2023, 24 (1); 53--74
    1508-2806
    2300-7036
    Pojawia się w:
    Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Equitable Colorings Of Corona Multiproducts Of Graphs
    Autorzy:
    Furmánczyk, Hanna
    Kubale, Marek
    Mkrtchyan, Vahan V.
    Powiązania:
    https://bibliotekanauki.pl/articles/31341573.pdf
    Data publikacji:
    2017-11-27
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    corona graph
    equitable chromatic number
    equitable coloring conjecture
    equitable graph coloring
    multiproduct of graphs
    NP-completeness
    polynomial algorithm
    Opis:
    A graph is equitably k-colorable if its vertices can be partitioned into k independent sets in such a way that the numbers of vertices in any two sets differ by at most one. The smallest k for which such a coloring exists is known as the equitable chromatic number of G and denoted by χ=(G). It is known that the problem of computation of χ=(G) is NP-hard in general and remains so for corona graphs. In this paper we consider the same model of coloring in the case of corona multiproducts of graphs. In particular, we obtain some results regarding the equitable chromatic number for the l-corona product G ◦l H, where G is an equitably 3- or 4-colorable graph and H is an r-partite graph, a cycle or a complete graph. Our proofs are mostly constructive in that they lead to polynomial algorithms for equitable coloring of such graph products provided that there is given an equitable coloring of G. Moreover, we confirm the Equitable Coloring Conjecture for corona products of such graphs. This paper extends the results from [H. Furmánczyk, K. Kaliraj, M. Kubale and V.J. Vivin, Equitable coloring of corona products of graphs, Adv. Appl. Discrete Math. 11 (2013) 103–120].
    Źródło:
    Discussiones Mathematicae Graph Theory; 2017, 37, 4; 1079-1094
    2083-5892
    Pojawia się w:
    Discussiones Mathematicae Graph Theory
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The smallest hard-to-color graphs for the classical, total and strong colorings of vertices
    Autorzy:
    Kubale, M.
    Manuszewski, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/206254.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    optymalizacja
    teoria grafów
    złożoność obliczeniowa
    benchmark
    chromatic number
    chromatic sum
    graph oring
    hard-to-color graph
    NP-completeness
    strong coloring
    Opis:
    : Let A(G) be the number of colors used by algorithm to color the vertices of graph G. A graph G is said to be hard-to-color (HC) (resp. slightly HC) if for every (resp. some) implementation of the algorithm A we have A(G) > chi(G), where chi(G) is the chromatic number of G. The study of HC graphs makes it possible design improved algorithms trying to avoid hard instances as far possible. Hard-to-color graphs are also good benchmarks for the evaluation of existing and future algorithms and provide an alternative way of assessing their quality. In this paper we demonstrate the smallest HC graphs for the best known coloring heuristics in classical applications, as well as when adapted to the chromatic sum coloring and strong coloring of vertices.
    Źródło:
    Control and Cybernetics; 1999, 28, 2; 355-365
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Towards the boundary between easy and hard control problems in multicast Clos networks
    Autorzy:
    Obszarski, P.
    Jastrzębski, A.
    Kubale, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/200819.pdf
    Data publikacji:
    2015
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    Clos-network
    2-cast call
    hypergraph edge coloring
    rearrageable network
    nonblocking network
    NP-completeness
    3-uniform hypergraph
    sieci
    połączenie sieciowe
    problem sieciowy
    Opis:
    In this article we study 3-stage Clos networks with multicast calls in general and 2-cast calls, in particular. We investigate various sizes of input and output switches and discuss some routing problems involved in blocking states. To express our results in a formal way we introduce a model of hypergraph edge-coloring. A new class of bipartite hypergraphs corresponding to Clos networks is studied. We identify some polynomially solvable instances as well as a number of NP-complete cases. Our results warn of possible troubles arising in the control of Clos networks even if they are composed of small-size switches in outer stages. This is in sharp contrast to classical unicast Clos networks for which all the control problems are polynomially solvable.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2015, 63, 3; 739-744
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
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