Wyniki wyszukiwania - Biblioteka Nauki

1

The Reconstruction of Polyominoes from Horizontal and Vertical Projections and Morphological Skeleton is NP-complete

100%

Hantos N. , Balázs P.

Fundamenta Informaticae

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2013

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tom Vol. 125, nr 3/4

343--359

EN

Reconstruction of binary images from their projections is one of the main tasks in many image processing areas, therefore determining the computational complexity of those problems is essential. The reconstruction complexity is highly dependent on the requirements of the image. In this paper, we will show that the reconstruction is NP-complete if the horizontal and vertical projections and the morphological skeleton of the image are given, and it is supposed that the image is 4-connected.

2

NP-completeness of weakly convex and convex dominating set decision problems

100%

Raczek J.

Opuscula Mathematica

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2004

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tom Vol. 24, no. 2

189-196

EN

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.

3

Euler Graphs, Triangle-Free Graphs and Bipartite Graphs in Switching Classes

100%

Hage J. , Harju T. , Welzl E.

Fundamenta Informaticae

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2003

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tom Vol. 58, nr 1

23--37

EN

In the context of graph transformations we look at the operation of switching, which can be viewed as a method for realizing global transformations of graphs through local transformations of the vertices. A switching class is then a set of graphs obtainable from a given start graph by applying the switching operation. Continuing the line of research in Ehrenfeucht, Hage, Harju and Rozenberg we consider the problem of detecting three kinds of graphs in switching classes. For all three we find algorithms running in time polynomial in the number of vertices in the graphs, although switching classes contain exponentially many graphs.

4

Balanced problems on graphs with categorization of edges

100%

Berežný Š. , Lacko V.

Discussiones Mathematicae Graph Theory

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2003

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tom 23

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nr 1

5-21

EN

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 𝓟 on G defined by a family of feasible sets 𝓓(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.

5

On the Power of P Systems with Contextual Rules

88%

Krishna S. N. , Lakshmanan K. , Rama R.

Fundamenta Informaticae

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2002

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tom Vol. 49, nr 1-3

167-178

EN

We consider P Systems with string objects which evolve by means of one-sided contextual rules and erasing contextual rules. The generative power of these systems with three or less than three membranes is investigated. We show that systems with three membranes characterize the family of recursively enumerable languages. When the string replication is used in one-sided contextual rules, these systems are able of solving NP-complete problems in linear time: this is exemplified with SAT and HPP.

6

Efficient list cost coloring of vertices and/or edges of bounded cyclicity graphs

88%

Giaro K. , Kubale M.

Discussiones Mathematicae Graph Theory

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2009

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tom 29

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nr 2

361-376

EN

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.

7

On the Complexity of the 3-Kernel Problem in Some Classes of Digraphs

75%

Hell P. , Hernández-Cruz C.

Discussiones Mathematicae Graph Theory

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2014

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tom 34

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nr 1

167-185

EN

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.

8

Equitable Colorings Of Corona Multiproducts Of Graphs

75%

Furmánczyk H. , Kubale M. , Mkrtchyan V. V.

Discussiones Mathematicae Graph Theory

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2017

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tom 37

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nr 4

1079-1094

EN

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].

9

Stable models for stubborn sets

75%

Varpaaniemi K.

Fundamenta Informaticae

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2000

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tom Vol. 43, Nr 1-4

355-375

EN

The stubborn set method is one of the methods that try to relieve the state space explosion problem that occurs in state space generation. Spending some time in looking for "good'" stubborn sets can pay off in the total time spent in generating a reduced state space. This article shows how the method can exploit tools that solve certain problems of logic programs. The restriction of a definition of stubbornness to a given state can be translated into a variable-free logic program. When a stubborn set satisfying additional constraints is wanted, the additional constraints should be translated, too. It is easy to make the translation in such a way that each acceptable stubborn set of the state is represented by at least one stable model of the program, each stable model of the program represents at least one acceptable stubborn set of the state, and for each pair in the representation relation, the number of certain atoms in the stable model is equal to the number of enabled transitions of the represented stubborn set. So, in order to find a stubborn set which is good w.r.t. the number of enabled transitions, it suffices to find a stable model which is good w.r.t. the number of certain atoms. The article also presents a new NP-completeness result concerning stubborn sets.

10

Vector Ambiguity and Freeness Problems in SL (2, Z)

75%

Ko S.-K. , Potapov I.

Fundamenta Informaticae

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2018

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tom Vol. 162, nr 2/3

161--182

EN

We study the vector ambiguity problem and the vector freeness problem in SL (2, Z). Given a finitely generated n x n matrix semigroup S and an n-dimensional vector x, the vector ambiguity problem is to decide whether for every target vector y = Mx, where M ∈ S, M is unique. We also consider the vector freeness problem which is to show that every matrix M which is transforming x to Mx has a unique factorization with respect to the generator of S. We show that both problems are NP-complete in SL (2, Z), which is the set of 2 x 2 integer matrices with determinant 1. Moreover, we generalize the vector ambiguity problem and extend to the finite and k-vector ambiguity problems where we consider the degree of vector ambiguity of matrix semigroups.

11

The Embedding Problem for Switching Classes of Graphs

75%

Ehrenfeucht A. , Hage J. , Harju T. , Rozenberg G.

Fundamenta Informaticae

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2006

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tom Vol. 74, nr 1

115-134

EN

In the context of graph transformation we look at the operation of switching, which can be viewed as a method for realizing global transformations of (group-labelled) graphs through local transformations of the vertices. In case vertices are given an identity, various relatively efficient algorithms exist for deciding whether a graph can be switched so that it contains some other graph, the query graph, as an induced subgraph. However, when considering graphs up to isomorphism, we immediately run into the graph isomorphism problem for which no efficient solution is known. Surprisingly enough however, in some cases the decision process can be simplified by transforming the query graph into a ``smaller'' graph without changing the answer. The main lesson learned is that the size of the query graph is not the dominating factor, but its cycle rank. Although a number of our results hold specifically for undirected, unlabelled graphs, we propose a more general framework and give many positive and negative results for more general cases, where the graphs are labelled with elements of a (finitely generated abelian) group.

12

Complexity Assessments for Decidable Fragments of Set Theory. I : A Taxonomy for the Boolean Case

75%

Cantone D. , De Domenico A. , Maugeri P. , Omodeo E. G.

Fundamenta Informaticae

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2021

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tom Vol. 181, nr 1

37--69

EN

We report on an investigation aimed at identifying small fragments of set theory (typically, sublanguages of Multi-Level Syllogistic) endowed with polynomial-time satisfiability decision tests, potentially useful for automated proof verification. Leaving out of consideration the membership relator ∈ for the time being, in this paper we provide a complete taxonomy of the polynomial and the NP-complete fragments involving, besides variables intended to range over the von Neumann set-universe, the Boolean operators ∪, ∩, \, the Boolean relators ⊆, ⊈,=, ≠, and the predicates ‘• = Ø’ and ‘Disj(•, •)’, meaning ‘the argument set is empty’ and ‘the arguments are disjoint sets’, along with their opposites ‘• ≠ Ø and ‘¬Disj(•, •)’. We also examine in detail how to test for satisfiability the formulae of six sample fragments: three sample problems are shown to be NP-complete, two to admit quadratic-time decision algorithms, and one to be solvable in linear time.

13

A note on hardness of multiprocessor scheduling with scheduling solution space tree

63%

Dwibedy D. , Mohanty R.

Computer Science

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2023

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tom T. 24 (1)

53--74

EN

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.

14

The smallest hard-to-color graphs for the classical, total and strong colorings of vertices

63%

Kubale M. , Manuszewski K.

Control and Cybernetics

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1999

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tom Vol. 28, no 2

355-365

EN

: 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.

15

Towards the boundary between easy and hard control problems in multicast Clos networks

63%

Obszarski P. , Jastrzębski A. , Kubale M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2015

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tom Vol. 63, nr 3

739--744

EN

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.

16

Szeregowanie rozrzedzonych systemów zadań jednostkowych 1- i 2-procesowych w oknach czasowych

51%

Giaro K. , Kubale M.

Automatyka / Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie

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2005

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tom T. 9, z. 1-2

85-94

PL

W artykule rozważono rozrzedzone systemy niepodzielnych zadań 1- i 2-procesorowych o jednostkowych czasach wykonywania. Przedstawiono wielomianowe algorytmy wykorzystujące programowanie dynamiczne, pozwalające na znalezienie optymalnego uszeregowania względem szerokiej rodziny funkcji kryterialnych. Stopień rozrzedzenia systemu zdefiniowano, posługując się jego modelem grafowym - w zakresie naszego zainteresowania leżą jedynie takie instancje problemów szeregowania, których modelami są grafy o ograniczonej liczbie cyklomatycznej. Istotnym elementem opracowanych procedur są algorytmy rozwiązujące pewne zagadnienia związane z wyszukiwaniem skojarzeń w grafach.

EN

In the paper sparse systems of dedicated 1- and 2-processor tasks with unit execution times are considered. Polynomial-time algorithms based on dynamic programming are given. These algorithms allow finding optimal solutions with respect to broad range of criterion functions. The sparsity of a system is measured in terms of the number of edges in the corresponding scheduling graph. More precisely, we are focused on graphs whose cyclomatic number is bounded by a constant. Our algorithms invoke procedures for finding maximal matching in graphs.

17

On the Complexity of Optimal Parallel Cooperative Path-Finding

51%

Surynek P.

Fundamenta Informaticae

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2015

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tom Vol. 137, nr 4

517--548

EN

A parallel version of the problem of cooperative path-finding (pCPF) is introduced in this paper. The task in CPF is to determine a spatio-temporal plan for each member of a group of agents. Each agent is given its initial location in the environment and its task is to reach the given goal location. Agents must avoid obstacles and must not collide with one another. The environment where agents are moving is modeled as an undirected graph. Agents are placed in vertices and they move along edges. At most one agent is placed in each vertex and at least one vertex remains unoccupied. An agent can only move into a currently unoccupied vertex in the standard version of CPF. In the parallel version, an agent can also move into a vertex being currently vacated by another agent supposing the character of this movement is not cyclic. The optimal pCPF where the task is to find the smallest possible solution of the makespan is particularly studied. The main contribution of this paper is the proof of NP-completeness of the decision version of the optimal pCPF. A reduction of propositional satisfiability (SAT) to the problem is used in the proof.