scholarly journals On BMRN*-colouring of planar digraphs

2021 ◽  
Vol vol. 23 no. 1 (Graph Theory) ◽  
Author(s):  
Julien Bensmail ◽  
Foivos Fioravantes
Keyword(s):  
Recent Work ◽  
Upper Bound ◽  
Special Focus ◽  
Np Hard ◽  
Scheduling Problems ◽  
Seminal Work ◽  
Complexity Result ◽  
International Audience ◽  
Tdma Scheduling ◽  
Planar Digraph

International audience In a recent work, Bensmail, Blanc, Cohen, Havet and Rocha, motivated by applications for TDMA scheduling problems, have introduced the notion of BMRN*-colouring of digraphs, which is a type of arc-colouring with particular colouring constraints. In particular, they gave a special focus to planar digraphs. They notably proved that every planar digraph can be 8-BMRN*-coloured, while there exist planar digraphs for which 7 colours are needed in a BMRN*-colouring. They also proved that the problem of deciding whether a planar digraph can be 3-BMRN*-coloured is NP-hard. In this work, we pursue these investigations on planar digraphs, in particular by answering some of the questions left open by the authors in that seminal work. We exhibit planar digraphs needing 8 colours to be BMRN*-coloured, thus showing that the upper bound of Bensmail, Blanc, Cohen, Havet and Rocha cannot be decreased in general. We also generalize their complexity result by showing that the problem of deciding whether a planar digraph can be k-BMRN*-coloured is NP-hard for every k ∈ {3,...,6}. Finally, we investigate the connection between the girth of a planar digraphs and the least number of colours in its BMRN*-colourings.

Some complexity results and an efficient algorithm for quay crane scheduling problem

2016 ◽  
Vol 08 (04) ◽  
pp. 1650058 ◽  
Author(s):  
Ming Liu ◽  
Shijin Wang ◽  
Feng Chu ◽  
Yinfeng Xu
Keyword(s):  
Precedence Constraint ◽  
Arbitrary Form ◽  
Scheduling Problem ◽  
Np Hard ◽  
Scheduling Problems ◽  
Quay Crane Scheduling ◽  
Crane Scheduling ◽  
Processing Times ◽  
Quay Cranes ◽  
Complexity Result

This paper investigates the quay crane scheduling problem (QCSP) at container ports, subject to arbitrary precedence constraint among vessel container tasks. Differing from classic machine scheduling problems, noncrossing constraint for quay cranes must be satisfied. This is because quay cranes work in parallel and they travel on a same rail (along the berth), to perform container unloading and loading tasks for vessels. Precedence relation in an arbitrary form is rarely investigated in the literature, however, it may be originated from reefers or dangerous cargo which requires high priority of processing, and yard stacking plan. We present the computational complexity for several problem variations. In particular, we show the QCSP, even without precedence constraint, is strongly NP-hard. This complexity result improves the state-of-the-art, in which the same problem is shown to be NP-hard in the ordinary sense. Besides, we also prove that for two parallel quay cranes, if the processing times of container tasks are ones and twos, then this scheduling problem is NP-hard. This result implies that the QCSP with arbitrary precedence constraint is very difficult to solve. A genetic algorithm is proposed to obtain near-optimal solutions. Computational experiments demonstrate the efficiency.

scholarly journals Stochastic Flips on Dimer Tilings

2010 ◽  
Vol DMTCS Proceedings vol. AM,... (Proceedings) ◽  
Author(s):  
Thomas Fernique ◽  
Damien Regnault
Keyword(s):  
Fixed Point ◽  
Markov Process ◽  
Upper Bound ◽  
Numerical Experiments ◽  
Triangular Grid ◽  
Expected Number ◽  
Worst Case ◽  
Average Case ◽  
International Audience

International audience This paper introduces a Markov process inspired by the problem of quasicrystal growth. It acts over dimer tilings of the triangular grid by randomly performing local transformations, called $\textit{flips}$, which do not increase the number of identical adjacent tiles (this number can be thought as the tiling energy). Fixed-points of such a process play the role of quasicrystals. We are here interested in the worst-case expected number of flips to converge towards a fixed-point. Numerical experiments suggest a $\Theta (n^2)$ bound, where $n$ is the number of tiles of the tiling. We prove a $O(n^{2.5})$ upper bound and discuss the gap between this bound and the previous one. We also briefly discuss the average-case.

scholarly journals Graphs with many vertex-disjoint cycles

2012 ◽  
Vol Vol. 14 no. 2 (Graph Theory) ◽  
Author(s):  
Dieter Rautenbach ◽  
Friedrich Regen
Keyword(s):  
Graph Theory ◽  
Upper Bound ◽  
Linear Time ◽  
Simple Extension ◽  
Disjoint Cycles ◽  
Cyclomatic Number ◽  
Finite Set ◽  
Extension Rule ◽  
International Audience ◽  
Vertex Disjoint

Graph Theory International audience We study graphs G in which the maximum number of vertex-disjoint cycles nu(G) is close to the cyclomatic number mu(G), which is a natural upper bound for nu(G). Our main result is the existence of a finite set P(k) of graphs for all k is an element of N-0 such that every 2-connected graph G with mu(G)-nu(G) = k arises by applying a simple extension rule to a graph in P(k). As an algorithmic consequence we describe algorithms calculating minmu(G)-nu(G), k + 1 in linear time for fixed k.

scholarly journals An Efficient Particle Swarm Optimizer with Application to Man-Day Project Scheduling Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Ruey-Maw Chen ◽  
Frode Eika Sandnes
Keyword(s):  
Project Scheduling ◽  
Particle Swarm ◽  
Scheduling Problem ◽  
Np Hard ◽  
Scheduling Problems ◽  
Particle Swarm Optimizer ◽  
Np Hard Problem ◽  
Hard Problems ◽  
Project Scheduling Problem ◽  
Mode Assignment

The multimode resource-constrained project scheduling problem (MRCPSP) has been confirmed to be an NP-hard problem. Particle swarm optimization (PSO) has been efficiently applied to the search for near optimal solutions to various NP-hard problems. MRCPSP involves solving two subproblems: mode assignment and activity priority determination. Hence, two PSOs are applied to each subproblem. A constriction PSO is proposed for the activity priority determination while a discrete PSO is employed for mode assignment. A least total resource usage (LTRU) heuristic and minimum slack (MSLK) heuristic ensure better initial solutions. To ensure a diverse initial collection of solutions and thereby enhancing the PSO efficiency, a best heuristic rate (HR) is suggested. Moreover, a new communication topology with random links is also introduced to prevent slow and premature convergence. To verify the performance of the approach, the MRCPSP benchmarks in PSPLIB were evaluated and the results compared to other state-of-the-art algorithms. The results demonstrate that the proposed algorithm outperforms other algorithms for the MRCPSP problems. Finally, a real-world man-day project scheduling problem (MDPSP)—a MRCPSP problem—was evaluated and the results demonstrate that MDPSP can be solved successfully.

scholarly journals ON SPANNERS OF GEOMETRIC GRAPHS

2009 ◽  
Vol 20 (01) ◽  
pp. 135-149 ◽  
Author(s):  
JOACHIM GUDMUNDSSON ◽  
MICHIEL SMID
Keyword(s):  
Real Number ◽  
Upper Bound ◽  
Weighted Graph ◽  
Geometric Graph ◽  
Geometric Graphs ◽  
Np Hard ◽  
Minimum Number ◽  
Np Hardness

Given a connected geometric graph G, we consider the problem of constructing a t-spanner of G having the minimum number of edges. We prove that for every real number t with [Formula: see text], there exists a connected geometric graph G with n vertices, such that every t-spanner of G contains Ω(n1+1/t) edges. This bound almost matches the known upper bound, which states that every connected weighted graph with n vertices contains a t-spanner with O(n1+2/(t-1)) edges. We also prove that the problem of deciding whether a given geometric graph contains a t-spanner with at most K edges is NP-hard. Previously, this NP-hardness result was only known for non-geometric graphs.

scholarly journals The infrastructures of mobile media: Towards a future reseach agenda

2013 ◽  
Vol 1 (1) ◽  
pp. 147-152 ◽  
Author(s):  
Heather A. Horst
Keyword(s):  
Recent Work ◽  
Mobile Communication ◽  
Global South ◽  
The Political ◽  
Third Wave ◽  
Communication Research ◽  
Mobile Media ◽  
Seminal Work ◽  
The Third

In this contribution to the inaugural issue of Mobile Media & Communication, I draw upon recent work on mobiles in the global south to illustrate how the ‘third wave’ of mobile communication research requires a renewed focus upon the political and economic dimensions of infrastructures and the subversion of the system by individuals, communities and organizations. Inspired by Susan Leigh Star’s seminal work on the importance of studying infrastructures, I suggest that mobile media scholarship should look to the changes in the technical, social, political, regulatory and other forms of infrastructures that the first two waves’ focus upon novel uses and consumers often rendered invisible.

scholarly journals Computing nilpotent quotients in finitely presented Lie rings

1997 ◽  
Vol Vol. 1 ◽  
Author(s):  
Csaba Schneider
Keyword(s):  
Abelian Group ◽  
Word Problem ◽  
Np Hard ◽  
Linear Combinations ◽  
Lie Ring ◽  
Lie Rings ◽  
Central Factor ◽  
Structure Theorems ◽  
International Audience ◽  
Finitely Presented

International audience A nilpotent quotient algorithm for finitely presented Lie rings over \textbfZ (and \textbfQ) is described. The paper studies the graded and non-graded cases separately. The algorithm computes the so-called nilpotent presentation for a finitely presented, nilpotent Lie ring. A nilpotent presentation consists of generators for the abelian group and the products expressed as linear combinations for pairs formed by generators. Using that presentation the word problem is decidable in L. Provided that the Lie ring L is graded, it is possible to determine the canonical presentation for a lower central factor of L. Complexity is studied and it is shown that optimising the presentation is NP-hard. Computational details are provided with examples, timing and some structure theorems obtained from computations. Implementation in C and GAP interface are available.

scholarly journals Saintsavaism(s) and Nationalism: An Overview of the Development of the Serbian Orthodox Phenomenon of Saintsavaism, with a Special Focus on the Contribution of Justin Popovic (1894–1979)

Exchange ◽  
2021 ◽  
Vol 50 (1) ◽  
pp. 77-98
Author(s):  
Neven Vukic
Keyword(s):  
Special Focus ◽  
Orthodox Church ◽  
Seminal Work ◽  
Philosophy Of Life ◽  
Guiding Principle ◽  
Yugoslav Wars ◽  
National Significance

Abstract This article provides a reflection on a relatively controversial phenomenon in the Serbian Orthodox Church, namely saintsavaism (serb. svetosavlje). The controversy accompanying the term is related to its association with the Serbian nationalism that erupted during the Yugoslav Wars of the 1990’s. This article aims to demonstrate that this particular interpretation of saintsavaism is, in fact, only one of at least four distinct understandings of the notion. Moreover, this article will argue that the author who contributed most significantly to the development of saintsavaism as the guiding principle of the Serbian Church to this day, namely, Justin Popovic (1894–1979), envisioned saintsavaism as, indeed, a totalizing worldview, and recognized its national significance, without, however, reducing it to simple ‘nationalism’. In order to make this case clear, the article will analyze in detail Popovic’s seminal work on saintsavaism (available only in Serbian), Saintsavaism as a Philosophy of Life (1953).

scholarly journals The resolving number of a graph Delia

2013 ◽  
Vol Vol. 15 no. 3 (Graph Theory) ◽  
Author(s):  
Delia Garijo ◽  
Antonio González ◽  
Alberto Márquez
Keyword(s):  
Graph Theory ◽  
Polynomial Time ◽  
Maximum Degree ◽  
Clique Number ◽  
Metric Dimension ◽  
Np Hard ◽  
Arbitrary Graph ◽  
International Audience ◽  
Graph Parameters ◽  
Two Parameters

Graph Theory International audience We study a graph parameter related to resolving sets and metric dimension, namely the resolving number, introduced by Chartrand, Poisson and Zhang. First, we establish an important difference between the two parameters: while computing the metric dimension of an arbitrary graph is known to be NP-hard, we show that the resolving number can be computed in polynomial time. We then relate the resolving number to classical graph parameters: diameter, girth, clique number, order and maximum degree. With these relations in hand, we characterize the graphs with resolving number 3 extending other studies that provide characterizations for smaller resolving number.

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