Recent Advances in Graph Partitioning

We survey recent trends in practical algorithms for balanced graph partitioning together with applications and future research directions

Low-Congestion Shortcut and Graph Parameters

Distributed graph algorithms in the standard CONGEST model often exhibit the time-complexity lower bound of Omega~(sqrt{n} + D) rounds for many global problems, where n is the number of nodes and D is the diameter of the input graph. Since such a lower bound is derived from special "hard-core" instances, it does not necessarily apply to specific popular graph classes such as planar graphs. The concept of low-congestion shortcuts is initiated by Ghaffari and Haeupler [SODA2016] for addressing the design of CONGEST algorithms running fast in restricted network topologies. Specifically, given a specific graph class X, an f-round algorithm of constructing shortcuts of quality q for any instance in X results in O~(q + f)-round algorithms of solving several fundamental graph problems such as minimum spanning tree and minimum cut, for X. The main interest on this line is to identify the graph classes allowing the shortcuts which are efficient in the sense of breaking O~(sqrt{n}+D)-round general lower bounds. In this paper, we consider the relationship between the quality of low-congestion shortcuts and three major graph parameters, chordality, diameter, and clique-width. The main contribution of the paper is threefold: (1) We show an O(1)-round algorithm which constructs a low-congestion shortcut with quality O(kD) for any k-chordal graph, and prove that the quality and running time of this construction is nearly optimal up to polylogarithmic factors. (2) We present two algorithms, each of which constructs a low-congestion shortcut with quality O~(n^{1/4}) in O~(n^{1/4}) rounds for graphs of D=3, and that with quality O~(n^{1/3}) in O~(n^{1/3}) rounds for graphs of D=4 respectively. These results obviously deduce two MST algorithms running in O~(n^{1/4}) and O~(n^{1/3}) rounds for D=3 and 4 respectively, which almost close the long-standing complexity gap of the MST construction in small-diameter graphs originally posed by Lotker et al. [Distributed Computing 2006]. (3) We show that bounding clique-width does not help the construction of good shortcuts by presenting a network topology of clique-width six where the construction of MST is as expensive as the general case

Investments in Modernization, Innovation and Gains in Productivity: Evidence from Firms in the Global Paper Industry

This paper examines the impact of investments in modernization and innovation on productivity in a sample of firms in the global pulp and paper industry. This industry is important because it has traditionally accounted for significant amounts of employment and capital investment in North America and Europe. In contrast to much of the existing literature which focuses on the impact of R&D and patents on firms’ performance and productivity, we examine data on actual investment transactions in four main areas of operations: (i) mechanical, (ii) chemicals, (iii) monitoring devices and (iv) information technology. We find that firms which made decisions to implement a greater number of investment transactions in modernization achieved higher productivity, and these estimated quantitative effects are greater than the impact of standard innovation variables such as patents and R&D. Investment transactions in the information technology and digital monitoring devices imparted a particularly noticeable boost to productivity. These results are obtained after controlling for other firm-specific variables such as capital-intensity and mergers and acquisitions. Two broad messages emerge from our study. First, firms’ decisions to undertake investments in modernization and various forms of incremental innovations appear to be critical for achieving gains in productivity. While these may typically generate small gains on a year-to-year basis, they can compound to form meaningful differences in performance, productivity and competitive position across firms in the longer-run. Second, for some of the traditional industries like pulp and paper, R&D and patents seem to be particularly poor indicators of innovation and, more generally, how firms go about achieving gains in productivity. While this paper focuses on the pulp and paper industry, our broad framework and methodology is general and can be applied to understanding firms’ strategies related to enhancing performance and productivity in a variety of industries.Pulp and paper industry; investment; modernization; innovation; productivity; organizational behavior

Rayleigh Approximation to Ground State of the Bose and Coulomb Glasses

Glasses are rigid systems in which competing interactions prevent simultaneous minimization of local energies. This leads to frustration and highly degenerate ground states the nature and properties of which are still far from being thoroughly understood. We report an analytical approach based on the method of functional equations that allows us to construct the Rayleigh approximation to the ground state of a two-dimensional (2D) random Coulomb system with logarithmic interactions. We realize a model for 2D Coulomb glass as a cylindrical type II superconductor containing randomly located columnar defects (CD) which trap superconducting vortices induced by applied magnetic field. Our findings break ground for analytical studies of glassy systems, marking an important step towards understanding their properties