Greedy algorithm

About: Greedy algorithm is a research topic. Over the lifetime, 15347 publications have been published within this topic receiving 393945 citations.

Electric vehicle charging station placement

Abstract: Transportation electrification is one of the essential components in the future smart city planning and electric vehicles (EVs) will be integrated into the transportation system seamlessly. Charging stations are the main source of energy for EVs and their locations are critical to the accessibility of EVs in a city. They should be carefully situated so that an EV can access a charging station within its driving range and cruise around anywhere in the city upon being recharged. In this paper, we formulate the Electric Vehicle Charging Station Placement Problem, in which we minimize the total construction cost subject to the constraints for the charging station coverage and the convenience of the drivers for EV charging. We study the properties of the problem, especially its NP-hardness, and propose an efficient greedy algorithm to tackle the problem. We perform a series of simulation whose results show that the greedy algorithm can result in solutions comparable to the mixed-integer programming approach and its computation time is much shorter.

Sum-Rate Analysis for Massive MIMO Downlink With Joint Statistical Beamforming and User Scheduling

Abstract: Statistical beamforming is an important technique for multi-user massive MIMO downlink, since it depends on the downlink channel covariance only. In this paper, we first derive an explicit analytical sum-rate expression for generic channel covariance-based beamforming scheme. Then, a low-complexity joint statistical beamforming and user scheduling algorithm via greedy search is proposed, where the beamforming is based on the signal-to-leakage-and-noise-ratio (SLNR) for closed-form design and tractable analysis, while the user scheduling is based on the derived sum-rate expression. Further, with the help of large-scale asymptotic simplifications and the introduction of the interference user number parameter, a simple analytical sum-rate expression of the joint algorithm is derived for channels with flat power beam spectrum. The expression explicitly exhibits the sum-rate behavior with respect to different network parameters and captures the effect of sum-rate-based user scheduling. Finally, simulation results are provided to verify our analytical results and to show the advantage of the proposed joint design compared with existing schemes.

Ordering heuristics for parallel graph coloring

Abstract: This paper introduces the largest-log-degree-first (LLF) and smallest-log-degree-last (SLL) ordering heuristics for parallel greedy graph-coloring algorithms, which are inspired by the largest-degree-first (LF) and smallest-degree-last (SL) serial heuristics, respectively. We show that although LF and SL, in practice, generate colorings with relatively small numbers of colors, they are vulnerable to adversarial inputs for which any parallelization yields a poor parallel speedup. In contrast, LLF and SLL allow for provably good speedups on arbitrary inputs while, in practice, producing colorings of competitive quality to their serial analogs. We applied LLF and SLL to the parallel greedy coloring algorithm introduced by Jones and Plassmann, referred to here as JP. Jones and Plassman analyze the variant of JP that processes the vertices of a graph in a random order, and show that on an O(1)-degree graph G=(V,E), this JP-R variant has an expected parallel running time of O(lgV/lglgV) in a PRAM model. We improve this bound to show, using work-span analysis, that JP-R, augmented to handle arbitrary-degree graphs, colors a graph G=(V,E) with degree Delta using Theta(V+E) work and O(lgV+ lg Delta . min sqrt-E, Delta +lg DeltaVlglgV) expected span. We prove that JP-LLF and JP-SLL --- JP using the LLF and SLL heuristics, respectively --- execute with the same asymptotic work as JP-R and only logarithmically more span while producing higher-quality colorings than JP-R in practice. We engineered an efficient implementation of JP for modern shared-memory multicore computers and evaluated its performance on a machine with 12 Intel Core-i7 (Nehalem) processor cores. Our implementation of JP-LLF achieves a geometric-mean speedup of 7.83 on eight real-world graphs and a geometric-mean speedup of 8.08 on ten synthetic graphs, while our implementation using SLL achieves a geometric-mean speedup of 5.36 on these real-world graphs and a geometric-mean speedup of 7.02 on these synthetic graphs. Furthermore, on one processor, JP-LLF is slightly faster than a well-engineered serial greedy algorithm using LF, and likewise, JP-SLL is slightly faster than the greedy algorithm using SL.

Data Assimilation in Reduced Modeling

Abstract: This paper considers the problem of optimal recovery of an element u of a Hilbert spaceH from measurements of the form ‘j(u), j = 1;:::;m, where the ‘j are known linear functionals on H. Problems of this type are well studied [18] and usually are carried out under an assumption that u belongs to a prescribed model class, typically a known compact subset ofH. Motivated by reduced modeling for solving parametric partial dierential equations, this paper considers another setting where the additional information about u is in the form of how well u can be approximated by a certain known subspaceVn ofH of dimensionn, or more generally, in the form of how well u can be approximated by each of a sequence of nested subspaces V0 V1 Vn with each Vk of dimension k. A recovery algorithm for the one-space formulation was proposed in [16]. Their algorithm is proven, in the present paper, to be optimal. It is also shown how the recovery problem for the one-space problem, has a simple formulation, if certain favorable bases are chosen to represent Vn and the measurements. The major contribution of the present paper is to analyze the multi-space case. It is shown that, in this multi-space case, the set of all u that satisfy the given information can be described as the intersection of a family of known ellipsoids in H. It follows that a near optimal recovery algorithm in the multi-space problem is provided by identifying any point in this intersection. It is easy to see that the accuracy of recovery of u in the multi-space setting can be much better than in the one-space problems. Two iterative algorithms based on alternating projections are proposed for recovery in the multi-space problem and one of them is analyzed in detail. This analysis includes an a posteriori estimate for the performance of the iterates. These a posteriori estimates can serve both as a stopping criteria in the algorithm and also as a method to derive convergence rates. Since the limit of the algorithm is a point in the intersection of the aforementioned ellipsoids, it provides a near optimal recovery for u.