Distributed Symmetry Breaking in Hypergraphs

Fundamental local symmetry breaking problems such as Maximal Independent Set (MIS) and coloring have been recognized as important by the community, and studied extensively in (standard) graphs. In particular, fast (i.e., logarithmic run time) randomized algorithms are well-established for MIS and $\Delta +1$-coloring in both the LOCAL and CONGEST distributed computing models. On the other hand, comparatively much less is known on the complexity of distributed symmetry breaking in {\em hypergraphs}. In particular, a key question is whether a fast (randomized) algorithm for MIS exists for hypergraphs. In this paper, we study the distributed complexity of symmetry breaking in hypergraphs by presenting distributed randomized algorithms for a variety of fundamental problems under a natural distributed computing model for hypergraphs. We first show that MIS in hypergraphs (of arbitrary dimension) can be solved in $O(\log^2 n)$ rounds ($n$ is the number of nodes of the hypergraph) in the LOCAL model. We then present a key result of this paper --- an $O(\Delta^{\epsilon}\text{polylog}(n))$-round hypergraph MIS algorithm in the CONGEST model where $\Delta$ is the maximum node degree of the hypergraph and $\epsilon > 0$ is any arbitrarily small constant. To demonstrate the usefulness of hypergraph MIS, we present applications of our hypergraph algorithm to solving problems in (standard) graphs. In particular, the hypergraph MIS yields fast distributed algorithms for the {\em balanced minimal dominating set} problem (left open in Harris et al. [ICALP 2013]) and the {\em minimal connected dominating set problem}. We also present distributed algorithms for coloring, maximal matching, and maximal clique in hypergraphs.Comment: Changes from the previous version: More references adde

Implicit Decomposition for Write-Efficient Connectivity Algorithms

The future of main memory appears to lie in the direction of new technologies that provide strong capacity-to-performance ratios, but have write operations that are much more expensive than reads in terms of latency, bandwidth, and energy. Motivated by this trend, we propose sequential and parallel algorithms to solve graph connectivity problems using significantly fewer writes than conventional algorithms. Our primary algorithmic tool is the construction of an $o(n)$-sized "implicit decomposition" of a bounded-degree graph $G$ on $n$ nodes, which combined with read-only access to $G$ enables fast answers to connectivity and biconnectivity queries on $G$. The construction breaks the linear-write "barrier", resulting in costs that are asymptotically lower than conventional algorithms while adding only a modest cost to querying time. For general non-sparse graphs on $m$ edges, we also provide the first $o(m)$ writes and $O(m)$ operations parallel algorithms for connectivity and biconnectivity. These algorithms provide insight into how applications can efficiently process computations on large graphs in systems with read-write asymmetry

Seismic design of reinforced concrete frames for minimum embodied CO2 emissions

Optimum structural design of reinforced concrete (RC) frames has been the focus of extensive research. Typically, previous studies set economic cost as the main design objective despite the fact that RC structures are major contributors of CO2 emissions. The limited number of studies examining optimum design of RC frames for minimum CO2 emissions do not address seismic design considerations. However, in many countries around the world, including most of the top-10 countries in CO2 emissions from cement production, RC structures must be designed against earthquake threat. To bridge this gap, the present study develops optimum seismic designs of RC frames for minimum cradle to gate embodied CO2 emissions and compares them with optimum designs based on construction cost. The aim is to identify efficient design practices that minimize the environmental impact of earthquake-resistant RC frames and examine the trade-offs between their cost and CO2 footprint. To serve this goal, an RC frame is optimally designed according to all ductility classes of Eurocode 8 and for various design peak ground accelerations (PGAs), concrete classes and materials embodied CO2 footprint scenarios. It is found that the minimum feasible CO2 emissions of RC frames strongly depend on the adopted ductility class in regions of high seismicity, where low ductility seismic design can generate up to 60% more CO2 emissions than designs for medium and high ductility. The differences reduce, however, as the level of seismicity decreases. Furthermore, CO2 emissions increase significantly with the design PGA. On the other hand, they are less sensitive to the applied concrete class. It is also concluded that, for medium to high values of the ratio of the unit environmental impact of reinforcing steel to the respective impact of concrete, the minimum CO2 seismic designs are very closely related to the minimum cost designs. However, for low values of the same ratio, the minimum cost design solutions can generate up to 13% more emissions than the minimum CO2 designs

Saliency Ratio and Power Factor of IPM Motors Optimally Designed for High Efficiency and Low Cost Objectives

This paper uses formal mathematical optimization techniques based on parametric finite-element-based computationally efficient models and differential evolution algorithms. For constant-power applications, in the novel approach described, three concurrent objective functions are minimized: material cost, losses, in order to ensure high efficiency, and the difference between the rated and the characteristic current, aiming to achieve very high constant-power flux-weakening range. Only the first two objectives are considered for constant-torque applications. Two types of interior permanent magnet rotors in a single- and double-layer V-shaped configuration are considered, respectively. The stator has the typical two slots per pole and phase distributed winding configuration. The results for the constant-torque design show that, in line with expectations, high efficiency and high power factor machines are more costly, and that the low-cost machines have poorer efficiency and power factor and most importantly, and despite a common misconception, the saliency ratio may also be lower in this case. For constant-power designs, the saliency ratio can be beneficial. Nevertheless, despite a common misconception, when cost is considered alongside performance as an objective, a higher saliency ratio does not necessarily improve the power factors of motors suitable for ideal infinite flux weakening