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Wyniki wyszukiwania dla: CHROMATIC COST COLORING, OPTIMUM COST CHROMATIC PARTITION, WEIGHTED GRAPH, BIPARTITE GRAPH, APPROXIMATION ALGORITHM, CHROMATIC COST 3-PSEUDOCOLORING
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Chromatic cost coloring of weighted bipartite graphs
PublikacjaGiven a graph G and a sequence of color costs C, the Cost Coloring optimization problem consists in finding a coloring of G with the smallest total cost with respect to C. We present an analysis of this problem with respect to weighted bipartite graphs. We specify for which finite sequences of color costs the problem is NP-hard and we present an exact polynomial algorithm for the other finite sequences. These results are then extended...
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A note on polynomial algorithm for cost coloring of bipartite graphs with Δ ≤ 4
PublikacjaIn 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 ∆≤4 can be solved in O(n^2) time. This extends Jansen’s result [K.Jansen,The optimum cost chromatic partition problem, in:...
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Infinite chromatic games
PublikacjaIn the paper we introduce a new variant of the graph coloring game and a new graph parameter being the result of the new game. We study their properties and get some lower and upper bounds, exact values for complete multipartite graphs and optimal, often polynomial-time strategies for both players provided that the game is played on a graph with an odd number of vertices. At the end we show that both games, the new and the classic...
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2-Coloring number revisited
Publikacja2-Coloring number is a parameter, which is often used in the literature to bound the game chromatic number and other related parameters. However, this parameter has not been precisely studied before. In this paper we aim to fill this gap. In particular we show that the approximation of the game chromatic number by the 2-coloring number can be very poor for many graphs. Additionally we prove that the 2-coloring number may grow...
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Interval Edge Coloring of Bipartite Graphs with Small Vertex Degrees
PublikacjaAn edge coloring of a graph G is called interval edge coloring if for each v ∈ V(G) the set of colors on edges incident to v forms an interval of integers. A graph G is interval colorable if there is an interval coloring of G. For an interval colorable graph G, by the interval chromatic index of G, denoted by χ'_i(G), we mean the smallest number k such that G is interval colorable with k colors. A bipartite graph G is called (α,β)-biregular...
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Equitable coloring of corona multiproducts of graphs
PublikacjaWe give some results regarding the equitable chromatic number for l-corona product of two graphs: G and 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 lead to polynomial algorithms for equitable coloring of such graph products provided that there is given an equitable coloring of G.
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On incidence coloring of coloring of complete multipartite and semicubic bipartite graphs
PublikacjaIn the paper, we show that the incidence chromatic number of a complete k-partite graph is at most ∆+2 (i.e., proving the incidence coloring conjecture for these graphs) and it is equal to ∆+1 if and only if the smallest part has only one vertex.
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T-colorings, divisibility and circular chromatic number
PublikacjaLet T be a T-set, i.e., a finite set of nonnegative integers satisfying 0 ∈ T, and G be a graph. In the paper we study relations between the T-edge spans espT (G) and espd⊙T (G), where d is a positive integer and d ⊙ T = {0 ≤ t ≤ d (max T + 1): d |t ⇒ t/d ∈ T} . We show that espd⊙T (G) = d espT (G) − r, where r, 0 ≤ r ≤ d − 1, is an integer that depends on T and G. Next we focus on the case T = {0} and show that espd⊙{0} (G) =...
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The Backbone Coloring Problem for Small Graphs
PublikacjaIn this paper we investigate the values of the backbone chromatic number, derived from a mathematical model for the problem of minimization of bandwidth in radio networks, for small connected graphs and connected backbones (up to 7 vertices). We study the relationship of this parameter with the structure of the graph and compare the results with the solutions obtained using the classical graph coloring algorithms (LF, IS), modified...
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Equitable coloring of corona products of graphs
PublikacjaIn this paper we consider an equitable coloring of some corona products of graphs G and H in symbols, G o H). In particular, we show that deciding the colorability of G o H is NP-complete even if G is 4-regular and H is K_2. Next, we prove exact values or upper bounds on the equitable chromatic number of G o H, where G is an equitably 3- or 4-colorable graph and H is an r-partite graph, a path, a cycle or a complete graph.
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Optimal backbone coloring of split graphs with matching backbones
PublikacjaFor a graph G with a given subgraph H, the backbone coloring is defined as the mapping c: V(G) -> N+ such that |c(u)-c(v)| >= 2 for each edge uv \in E(H) and |c(u)-c(v)| >= 1 for each edge uv \in E(G). The backbone chromatic number BBC(G;H) is the smallest integer k such that there exists a backbone coloring with max c(V(G)) = k. In this paper, we present the algorithm for the backbone coloring of split graphs with matching backbone.
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The Backbone Coloring Problem for Bipartite Backbones
PublikacjaLet G be a simple graph, H be its spanning subgraph and λ≥2 be an integer. By a λ -backbone coloring of G with backbone H we mean any function c that assigns positive integers to vertices of G in such a way that |c(u)−c(v)|≥1 for each edge uv∈E(G) and |c(u)−c(v)|≥λ for each edge uv∈E(H) . The λ -backbone chromatic number BBCλ(G,H) is the smallest integer k such that there exists a λ -backbone coloring c of G with backbone H satisfying...
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Edge coloring of graphs of signed class 1 and 2
PublikacjaRecently, Behr (2020) introduced a notion of the chromatic index of signed graphs and proved that for every signed graph (G, σ) it holds that ∆(G) ≤ χ′(G,σ) ≤ ∆(G) + 1, where ∆(G) is the maximum degree of G and χ′ denotes its chromatic index. In general, the chromatic index of (G, σ) depends on both the underlying graph G and the signature σ. In the paper we study graphs G for which χ′(G, σ) does not depend on σ. To this aim we...
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Minimum order of graphs with given coloring parameters
PublikacjaA complete k-coloring of a graph G=(V,E) is an assignment F: V -> {1,...,k} of colors to the vertices such that no two vertices of the same color are adjacent, and the union of any two color classes contains at least one edge. Three extensively investigated graph invariants related to complete colorings are the minimum and maximum number of colors in a complete coloring (chromatic number χ(G) and achromatic number ψ(G), respectively),...
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Dynamic coloring of graphs
PublikacjaDynamics is an inherent feature of many real life systems so it is natural to define and investigate the properties of models that reflect their dynamic nature. Dynamic graph colorings can be naturally applied in system modeling, e.g. for scheduling threads of parallel programs, time sharing in wireless networks, session scheduling in high-speed LAN's, channel assignment in WDM optical networks as well as traffic scheduling. In...
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Eqiuitable coloring of corona products of cubic graphs is harder than ordinary coloring
PublikacjaA graph is equitably k-colorable if its vertices can be partitioned into k independent sets in such a way that the number 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. In this paper the problem of determinig the equitable coloring number for coronas of cubic graphs is studied. Although the problem of ordinary coloring of coronas...
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The computational complexity of the backbone coloring problem for planar graphs with connected backbones
PublikacjaIn the paper we study the computational complexity of the backbone coloring problem for planar graphs with connected backbones. For every possible value of integer parameters λ≥2 and k≥1 we show that the following problem: Instance: A simple planar graph GG, its connected spanning subgraph (backbone) HH. Question: Is there a λ-backbone coloring c of G with backbone H such that maxc(V(G))≤k? is either NP-complete or polynomially...
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A 27/26-approximation algorithm for the chromatic sum coloring of bipartitegraphs
PublikacjaWe consider the CHROMATIC SUM PROBLEM on bipartite graphs which appears to be much harder than the classical CHROMATIC NUMBER PROBLEM. We prove that the CHROMATIC SUM PROBLEM is NP-complete on planar bipartite graphs with Delta less than or equal to 5, but polynomial on bipartite graphs with Delta less than or equal to 3, for which we construct an O(n(2))-time algorithm. Hence, we tighten the borderline of intractability for this...
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Relations between the domination parameters and the chromatic index of a graph
PublikacjaIn this paper we show bounds for the sum and the product of the domination parameters and the chromatic index of a graph. We alsopresent some families of graphs for which these bounds are achieved.
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Total chromatic sum for trees
PublikacjaThe total chromatic sum of a graph is the minimum sum of colors (natural numbers) taken over all proper colorings of vertices and edges of a graph. We provide infinite families of trees for which the minimum number of colors to achieve the total chromatic sum is equal to the total chromatic number. We construct infinite families of trees for which these numbers are not equal, disproving the conjecture from 2012.
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On minimum cost edge searching
PublikacjaWe consider the problem of finding edge search strategies of minimum cost. The cost of a search strategy is the sum of searchers used in the clearing steps of the search. One of the natural questions is whether it is possible to find a search strategy that minimizes both the cost and the number of searchers used to clear a given graph G. We call such a strategy ideal. We prove, by an example, that ideal search strategies do not...
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Computer experiments with a parallel clonal selection algorithm for the graph coloring problem
PublikacjaArtificial immune systems (AIS) are algorithms that are based on the structure and mechanisms of the vertebrate immune system. Clonal selection is a process that allows lymphocytes to launch a quick response to known pathogens and to adapt to new, previously unencountered ones. This paper presents a parallel island model algorithm based on the clonal selection principles for solving the Graph Coloring Problem. The performance of...
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Graph classes generated by Mycielskians
PublikacjaIn this paper we use the classical notion of weak Mycielskian M'(G) of a graph G and the following sequence: M'_{0}(G) =G, M'_{1}(G)=M'(G), and M'_{n}(G)=M'(M'_{n−1}(G)), to show that if G is a complete graph oforder p, then the above sequence is a generator of the class of p-colorable graphs. Similarly, using Mycielskian M(G) we show that analogously defined sequence is a generator of the class consisting of graphs for which the...
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Sławomir Jerzy Ambroziak dr hab. inż.
OsobySławomir J. Ambroziak urodził się w 1982 r. Uzyskał tytuł zawodowy magistra inżyniera w zakresie systemów i usług radiokomunikacyjnych w roku 2008, w 2013 r. uzyskał stopień doktora nauk technicznych w dyscyplinie telekomunikacja, w specjalności radiokomunikacja, natomiast w 2020 r. uzyskał stopień doktora habilitowanego. Od 2008 r. jest pracownikiem Katedry Systemów i Sieci Radiokomunikacyjnych na Wydziale Elektroniki, Telekomunikacji...
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Parallel tabu search for graph coloring problem
PublikacjaTabu search is a simple, yet powerful meta-heuristic based on local search that has been often used to solve combinatorial optimization problems like the graph coloring problem. This paper presents current taxonomy of patallel tabu search algorithms and compares three parallelization techniques applied to Tabucol, a sequential TS algorithm for graph coloring. The experimental results are based on graphs available from the DIMACS...
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Parallel immune system for graph coloring
PublikacjaThis paper presents a parallel artificial immune system designed forgraph coloring. The algorithm is based on the clonal selection principle. Each processor operates on its own pool of antibodies and amigration mechanism is used to allow processors to exchange information. Experimental results show that migration improves the performance of the algorithm. The experiments were performed using a high performance cluster on a set...
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Chromatic scheduling in a cyclic open shop
PublikacjaPraca jest poświęcona złożoności obliczeniowej problemu cyklicznego szeregowania w systemie otwartym. Autorzy analizując wykazują, że problem jest NP-trudny dla 3 procesorów i konstruują algorytm dokładny dla przypadku dwóch procesorów.Ponadto analizowany jest zwarty wariant cyklicznego systemu otwartego. W tym przypadku autorzy pokazują, że już szeregowanie na dwóch procesorach prowadzi do problemu NP-trudnego.
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Krzysztof Cwalina dr inż.
OsobyKrzysztof Kamil Cwalina w 2013 r. uzyskał tytuł inżyniera na Wydziale Elektroniki, Telekomunikacji i Informatyki Politechniki Gdańskiej; w 2014 r. uzyskał tytuł magistra inżyniera, a w 2017 r. otrzymał stopień doktora nauk technicznych w dyscyplinie: telekomunikacja, także na WETI PG. Aktualnie pracuje na stanowisku adiunkta w Katedrze Systemów i Sieci Radiokomunikacyjnych Wydziału Elektroniki, Telekomunikacji i Informatyki Politechniki...
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Recent progress in research on the cutting processes of wood. A review COST Action E35 2004-2008: Wood machining - micromechanics and fracture
PublikacjaZaprezentowano postępy w badaniach przecinania drewna ze szczególnym uwzględnieniem nowych metod dedykowanych zwiększeniu wydajności materiałowej w tartacznictwie. Zademonstrowano przydatność współczesnej mechaniki pękania do szacowania mocy skrawania dla pił, których wartości rozwarcia są różne od pił użytych w badaniach skrawalnościowych. W tych ostatnich wyznaczano wiązkość materiału obrabianego oraz naprężenia tnące. Badania...
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Recent progress in research on the cutting processes of wood. A review COST Action E35 2004-2008: Wood machining - micromechanics and fracture
PublikacjaZaprezentowano postępy w badaniach przecinania drewna ze szczególnym uwzględnieniem nowych metod dedykowanych zwiększeniu wydajności materiałowej w tartacznictwie. Zademonstrowano przydatność współczesnej mechaniki pękania do szacowania mocy skrawania dla pił, których wartości rozwarcia są różne od pił użytych w badaniach skrawalnościowych. W tych ostatnich wyznaczano wiązkość materiału obrabianego oraz naprężenia tnące. Badania...
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Product Graph Invariants with Applications in the Theory of Information
PublikacjaThere are a large number of graph invariants. In the paper, we consider some of them, e.g. the independence and chromatic numbers. It is well know that we cannot efficiently calculate these numbers for arbitrary graphs. In the paper we present relations between these invariants and concepts from the theory of information. Concepts such as source coding and transmission over a noisy channel with zero probability of error are modeled...
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THE COST ANALYSIS OF CORROSION PROTECTION SOLUTIONS FOR STEEL COMPONENTS IN TERMS OF THE OBJECT LIFE CYCLE COST
PublikacjaSteel materials, due to their numerous advantages - high availability, easiness of processing and possibility of almost any shaping are commonly applied in construction for carrying out basic carrier systems and auxiliary structures. However, the major disadvantage of this material is its high corrosion susceptibility, which depends strictly on the local conditions of the facility and the applied type of corrosion protection system....
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Discussiones Mathematicae Graph Theory
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A better practical algorithm for distributed graph coloring
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Distributed largest-first algorithm for graph coloring.
PublikacjaW artykule zaprezentowano rozproszony, probabilistyczny algorytm kolorowania grafów. Kolorowanie uzyskane jest optymalne lub prawie optymalne dla takich klas grafów jak koła dwudzielne, gąsienice czy korony. Udowodniono, że algorytm ten działa w czasie O(D^2 log n) rund dla dowolnego grafu n wierzchołkowegoo stopniu maksymalnym D.
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Interval incidence graph coloring
PublikacjaIn this paper we introduce a concept of interval incidence coloring of graphs and survey its general properties including lower and upper bounds on the number of colors. Our main focus is to determine the exact value of the interval incidence coloring number χii for selected classes of graphs, i.e. paths, cycles, stars, wheels, fans, necklaces, complete graphs and complete k-partite graphs. We also study the complexity of the...
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The circular chromatic index of some class 2 graphs
PublikacjaW artykule został wyznaczony cyrkularny indeks chromatyczny dla dwóch rodzin grafów klasy 2. Co więcej, podano nie trywialne oszacowania tego parametru dla snarków Isaacsa i Goldberga. Na koniec artykułu rozważana jest złożoność obliczeniowa problemów związanych z cyrkularnym kolorowaniem krawędzi.
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Edge-chromatic sum of trees and bounded cyclicity graphs
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Efficient list cost coloring of vertices and/or edges of bounded cyclicity graphs
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Efficient list cost coloring of vertices and/or edges of bounded cyclicity graphs
PublikacjaW artykule rozważamy listowo-kosztowe kolorowanie wierzchołków i krawędzi grafu w modelu wierzchołkowym, krawędziowym, totalnym i pseudototalnym. Stosujemy programowanie dynamiczne w celu otrzymania algorytmów wielomianowych dla drzew. Następnie uogólniamy to podejście na dowolne grafy z ograniczonymi liczbami cyklomatycznymi i na ich multikolorowania.
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Restrained differential of a graph
PublikacjaGiven a graph $G=(V(G), E(G))$ and a vertex $v\in V(G)$, the {open neighbourhood} of $v$ is defined to be $N(v)=\{u\in V(G) :\, uv\in E(G)\}$. The {external neighbourhood} of a set $S\subseteq V(G)$ is defined as $S_e=\left(\cup_{v\in S}N(v)\right)\setminus S$, while the \emph{restrained external neighbourhood} of $S$ is defined as $S_r=\{v\in S_e : N(v)\cap S_e\neq \varnothing\}$. The restrained differential of a graph $G$ is...
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Interval incidence coloring of bipartite graphs
PublikacjaIn this paper we study the problem of interval incidence coloring of bipartite graphs. We show the upper bound for interval incidence coloring number (χii) for bipartite graphs χii≤2Δ, and we prove that χii=2Δ holds for regular bipartite graphs. We solve this problem for subcubic bipartite graphs, i.e. we fully characterize the subcubic graphs that admit 4, 5 or 6 coloring, and we construct a linear time exact algorithm for subcubic...
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TOTAL DOMINATION MULTISUBDIVISION NUMBER OF A GRAPH
PublikacjaThe domination multisubdivision number of a nonempty graph G was defined in [3] as the minimum positive integer k such that there exists an edge which must be subdivided k times to increase the domination number of G. Similarly we define the total domination multisubdivision number msd_t (G) of a graph G and we show that for any connected graph G of order at least two, msd_t (G) ≤ 3. We show that for trees the total domination...
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Cost assessment of computer security activities
PublikacjaComprehensive cost-benefit analysis plays a crucial role in the decision-making process when it comes to investments in information security solutions. The cost of breaches needs to be analysed in the context of spending on protection measures. However, no methods exist that facilitate the quick and rough prediction of true expenditures on security protection systems. Rafal Leszczyna of Gdansk University of Technology presents...
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Journal of Benefit-Cost Analysis
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Cost Effectiveness and Resource Allocation
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A graph coloring approach to scheduling of multiprocessor tasks on dedicated machines with availability constraints
PublikacjaWe address a generalization of the classical 1- and 2-processor unit execution time scheduling problem on dedicated machines. In our chromatic model of scheduling machines have non-simultaneous availability times and tasks have arbitrary release times and due dates. Also, the versatility of our approach makes it possible to generalize all known classical criteria of optimality. Under these stipulations we show that the problem...
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Low-Cost Multi-Objective Optimization of Antennas By Means Of Generalized Pareto Ranking Bisection Algorithm
PublikacjaThis paper introduces a generalized Pareto ranking bisection algorithm for low-cost multi-objective design optimization of antenna structures. The algorithm allows for identifying a set of Pareto optimal sets of parameters (that represent the best trade-offs between considered objectives) by iterative partitioning of the intervals connecting previously found designs and executing a Pareto-ranking-based poll search. The initial...
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Koala graph coloring library: an open graph coloring library for real-world applications
PublikacjaPomimo intensywnej pracy naukowej na polu kolorowania grafów, nie jest znana kompletna i dedykowana biblioteka programistyczna. Celem artykułu jest zaproponowanie architektury takiej biblioteki. Celem jest spełnienie oczekiwań wypływających z rzeczywistych zastosowań, w szczególności spełnienie potrzeb wydajnościowych. Zaimplementowano szereg algorytmów cheurystycznego kolorowania grafów. Przyjętym językiem programowania jest C++....
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Approximation Strategies for Generalized Binary Search in Weighted Trees
PublikacjaWe consider the following generalization of the binary search problem. A search strategy is required to locate an unknown target node t in a given tree T. Upon querying a node v of the tree, the strategy receives as a reply an indication of the connected component of T\{v} containing the target t. The cost of querying each node is given by a known non-negative weight function, and the considered objective is to minimize the total...