Constant factor approximation for the weighted partial degree bounded edge packing problem

In the partial degree bounded edge packing problem (PDBEP), the input is an undirected graph \(G=(V,E)\) with capacity \(c_v\in {\mathbb {N}}\) on each vertex v. The objective is to find a feasible subgraph \(G'=(V,E')\) maximizing \(|E'|\), where \(G'\) is said to be feasible if for each \(e=\{u,v\}\in E'\), \(\deg _{G'}(u)\le c_u\) or \(\deg _{G'}(v)\le c_v\). In the weighted version of the problem, additionally each edge \(e\in E\) has a weight w(e) and we want to find a feasible subgraph \(G'=(V,E')\) maximizing \(\sum _{e\in E'} w(e)\). The problem is already NP-hard if \(c_v = 1\) for all \(v\in V\) (Zhang in: Proceedings of the joint international conference on frontiers in algorithmics and algorithmic aspects in information and management, FAW-AAIM 2012, Beijing, China, May 14–16, pp 359–367, 2012). In this paper, we introduce a generalization of the PDBEP problem. We let the edges have weights as well as demands, and we present the first constant-factor approximation algorithms for this problem. Our results imply the first constant-factor approximation algorithm for the weighted PDBEP problem, improving the result of Aurora et al. (FAW-AAIM 2013) who presented an \(O(\log n)\)-approximation for the weighted case. We also study the weighted PDBEP problem on hypergraphs and present a constant factor approximation if the maximum degree of the hypergraph is bounded above by a constant. We study a generalization of the weighted PDBEP problem with demands where each edge additionally specifies whether it requires at least one, or both its end-points to not exceed the capacity. The objective is to pick a maximum weight subset of edges. We give a constant factor approximation for this problem. We also present a PTAS for the weighted PDBEP problem with demands on H-minor free graphs, if the demands on the edges are bounded by polynomial. We show that the PDBEP problem is APX-hard even for bipartite graphs with \(c_v = 1, \; \forall v\in V\) and having degree at most 3.     

An $$O(|E(G)|^2)$$ algorithm for recognizing Pfaffian graphs of a type of bipartite graphs

A graph \(G=(V,E)\) with even number vertices is called Pfaffian if it has a Pfaffian orientation, namely it admits an orientation such that the number of edges of any M-alternating cycle which have the same direction as the traversal direction is odd for some perfect matching M of the graph G. In this paper, we obtain a necessary and sufficient condition of Pfaffian graphs in a type of bipartite graphs. Then, we design an \(O(|E(G)|^2)\) algorithm for recognizing Pfaffian graphs in this class and constructs a Pfaffian orientation if the graph is Pfaffian. The results improve and generalize some known results.     

Neighbor sum distinguishing list total coloring of subcubic graphs

Let \(G=(V, E)\) be a simple graph and denote the set of edges incident to a vertex v by E(v). The neighbor sum distinguishing (NSD) total choice number of G, denoted by \(\mathrm{ch}_{\Sigma }^{t}(G)\), is the smallest integer k such that, after assigning each \(z\in V\cup E\) a set L(z) of k real numbers, G has a total coloring \(\phi \) satisfying \(\phi (z)\in L(z)\) for each \(z\in V\cup E\) and \(\sum _{z\in E(u)\cup \{u\}}\phi (z)\ne \sum _{z\in E(v)\cup \{v\}}\phi (z)\) for each \(uv\in E\). In this paper, we propose some reducible configurations of NSD list total coloring for general graphs by applying the Combinatorial Nullstellensatz. As an application, we present that \(\mathrm{ch}^{t}_{\Sigma }(G)\le \Delta (G)+3\) for every subcubic graph G.     

The matching extension problem in general graphs is co-NP-complete

A simple connected graph G with 2n vertices is said to be k-extendable for an integer k with \(0<k<n\) if G contains a perfect matching and every matching of cardinality k in G is a subset of some perfect matching. Lakhal and Litzler (Inf Process Lett 65(1):11–16, 1998) discovered a polynomial algorithm that decides whether a bipartite graph is k-extendable. For general graphs, however, it has been an open problem whether there exists a polynomial algorithm. The new result presented in this paper is that the extendability problem is co-NP-complete.     

A quadratic time exact algorithm for continuous connected 2-facility location problem in trees

This paper studies the continuous connected 2-facility location problem (CC2FLP) in trees. Let \(T = (V, E, c, d, \ell , \mu )\) be an undirected rooted tree, where each node \(v \in V\) has a weight \(d(v) \ge 0\) denoting the demand amount of v as well as a weight \(\ell (v) \ge 0\) denoting the cost of opening a facility at v, and each edge \(e \in E\) has a weight \(c(e) \ge 0\) denoting the cost on e and is associated with a function \(\mu (e,t) \ge 0\) denoting the cost of opening a facility at a point x(e, t) on e where t is a continuous variable on e. Given a subset \(\mathcal {D} \subseteq V\) of clients, and a subset \(\mathcal {F} \subseteq \mathcal {P}(T)\) of continuum points admitting facilities where \(\mathcal {P}(T)\) is the set of all the points on edges of T, when two facilities are installed at a pair of continuum points \(x_1\) and \(x_2\) in \(\mathcal {F}\), the total cost involved in CC2FLP includes three parts: the cost of opening two facilities at \(x_1\) and \(x_2\), K times the cost of connecting \(x_1\) and \(x_2\), and the cost of all the clients in \(\mathcal {D}\) connecting to some facility. The objective is to open two facilities at a pair of continuum points in \(\mathcal {F}\) to minimize the total cost, for a given input parameter \(K \ge 1\). This paper focuses on the case of \(\mathcal {D} = V\) and \(\mathcal {F} = \mathcal {P}(T)\). We first study the discrete version of CC2FLP, named the discrete connected 2-facility location problem (DC2FLP), where two facilities are restricted to the nodes of T, and devise a quadratic time edge-splitting algorithm for DC2FLP. Furthermore, we prove that CC2FLP is almost equivalent to DC2FLP in trees, and develop a quadratic time exact algorithm based on the edge-splitting algorithm. Finally, we adapt our algorithms to the general case of \(\mathcal {D} \subseteq V\) and \(\mathcal {F} \subseteq \mathcal {P}(T)\).     

Reliability evaluation of a multicast over coded packet networks

Network coding is a generalization of conventional routing methods that allows a network node to code information flows before forwarding them. While it has been theoretically proved that network coding can achieve maximum network throughput, theoretical results usually do not consider the stochastic nature in information processing and transmission, especially when the capacity of each arc becomes stochastic due to failure, attacks, or maintenance. Hence, the reliability measurement of network coding becomes an important issue to evaluate the performance of the network under various system settings. In this paper, we present analytical expressions to measure the reliability of multicast communications in coded networks, where network coding is most promising. We define the probability that a multicast rate can be transmitted through a coded packet network under a total transmission cost constraint as the reliability metric. To do this, we first introduce an exact mathematical formulation to construct multicast connections over coded packet networks under a limited transmission cost. We then propose an algorithm based on minimal paths to calculate the reliability measurement of multicast connections and analyze the complexity of the algorithm. Our results show that the reliability of multicast routing with network coding improved significantly compared to the case of multicast routing without network coding.     

Does the capital of social capital matter? Relational resources of the board and the performance of Brazilian companies

Based on theories of social capital, in this study, we seek to assess the impact of a board’s social capital on the market value of companies listed on the Brazilian stock exchange. As our indicator of social capital, we use the relational resources identified in the direct, indirect and heterogeneous ties of the board. Employing panel data from 508 observations, our results indicate that heterogeneous relational resources have a stronger and more significant influence than the resources available from board members’ direct relationships. Additionally, as the effects of board interlock are endogenously determined by several factors related to the firm level, we seek to mitigate the endogeneity problem using models of instrumental variables and simultaneous equations. Our hypotheses were consistent after controlling for endogeneity. We also check whether the board’s social capital could present a U-inverted effect on the market value. This relationship was only plausible in social capital by indirect ties. Finally, we isolate the effect of relational resources within and between industries on Tobin’s Q. There was no significant effect through interlocks within the same industry. However, ties with companies in several other industries were significant.     

On the relationship between compliance with recommendations on the audit committee of codes of good practices and financial reporting quality

Codes of good practices provide a soft alternative to the hard legislation approach to corporate governance. These codes include a set of recommendations that companies are expected to follow in order to enhance governance structures and practices. Some of these recommendations specifically aim to improve the effectiveness of the audit committee. We investigate the relationship between the level of compliance with recommendations on the audit committee of the Spanish Unified Code and financial reporting quality, as measured by discretionary accruals and by the opinion of the audit report. We use a sample of companies listed in the Spanish stock market for the years between 2007 and 2013. Results show a strong and positive relationship between the level of compliance with recommendations and the quality of financial reporting. We also report significant results for some specific recommendations. These results are robust to various checks. Therefore, the level of compliance with recommendations on the audit committee might provide a feasible and reliable indicator of the quality of financial reports released by the company.     

Performance management change in archaeological sites: The case of Herculaneum Conservation Project

This study focuses on the issues relating to the implementation of management accounting systems in complex settings such as archeological sites. The aim is to understand the conditions under which the implementation of performance management systems (PMS) may enable cultural organizations to fulfil their multiple objectives and the factors which play a crucial role in such dynamics. Focusing on the Herculaneum Conservation Project (HCP) the study explains how PMS came to be implemented having been made acceptable to all parties involved. The Middle Range Theory as developed by Broadbent and Laughlin (Accounting control and controlling accounting: interdisciplinary and critical perspectives, Bingley, Emerald, 2013) was utilized to explore how the PMS change took place in the HCP, and focus on the factors influencing this process. The findings reveal that the change in the PMS benefited from the involvement of a multidisciplinary Specialist Work Group. This involvement reduced the natural tendency to resist the forces of change and increased the commitment of the various groups of stakeholders to the new culture. The findings reveal how PMS were developed in the context of a multifaceted approach to change, allowing us to draw both theoretical and practical lessons that may be brought to bear in other complex contexts.     

FPT-algorithms for some problems related to integer programming

This paper studies a new version of the location problem called the mixed center location problem. Let P be a set of n points in the plane. We first consider the mixed 2-center problem, where one of the centers must be in P, and we solve it in \(O(n^2\log n)\) time. Second, we consider the mixed k-center problem, where m of the centers are in P, and we solve it in \(O(n^{m+O(\sqrt{k-m})})\) time. Motivated by two practical constraints, we propose two variations of the problem. Third, we present a 2-approximation algorithm and three heuristics solving the mixed k-center problem (\(k>2\)).