The potential of greed for independence

A channel scheduling problem for a given graph G(V,E) is to select a subset E′ of edges of E and assign channel to each one in E′ under the restriction that all edges of E′ are interference free. We introduce the notion of two sides approximation for the channel scheduling problem. A pair of parameters (f,g) controls the accuracy of approximation in this paper. A (f,g)-approximation satisfies \(\sum_{e\in E'}W(e)\ge{\sum_{e\in Opt}W(e)\over f}\) and \(\sum_{e\in E-E'}W(e)\le g\sum_{e\in E- Opt^*}W(e)\), where Opt * is the set of edges assigned channels in an optimal solution, and W(e) is the weight of edge e. An f-approximation satisfies \(\sum_{e\in E'}W(e)\ge{\sum_{e\in Opt}W(e)\over f}\). We show that a simple greedy algorithm can obtain an (O(1), O(1))-approximation for the single channel scheduling problem. In many cases, the greedy algorithms gives much more accurate result than the worst ratio. Furthermore, we develop an \(|E|^{O({1\over \epsilon})}\) time (1 − ε, O(1))-approximation algorithm for the single channel scheduling problem. We also show that a simple greedy algorithm can obtain an O(1)-approximation for the multi-channel scheduling problem which satisfies \(\sum_{e\in E'}W(e)\ge{\sum_{e\in Opt}W(e)\over \Omega(1)}\). We also develop a \(|E|^{O({d\over \epsilon})}\) time (1 − ε)-approximation algorithm the multi-channel scheduling problem, where d is the number of channels. This improves the existing approximation scheme for multi-channel scheduling problem with \(|E|^{O({d\over \epsilon^2})}\) time by Cheng et al. We also develop a polynomial time constant factor greedy approximation algorithm for the multi-channel scheduling that allows variate radii of interference among those nodes.

Replicating of objects at multi nodes has been considered a promising technique for decreasing access cost and network traffic for a large distributed systems like Data Grids. In this paper we propose Optimal Placement of Replicas (OPR) algorithm with the objective of minimizing the total replication cost including communication and storage cost, given that a maximum of k replicas are allowed in a tree data grid with n nodes and height h. OPR has time complexity of O(nhk), which is the lowest time complexity compared with the other algorithms with the same objective function in the past literature. In addition, two greedy algorithms, namely, Greedy Algorithm (GA) and Simple Greedy Algorithm (SGA) are proposed for near optimal placement of k replicas with the lower time complexity compared with that of OPR. We evaluate the proposed algorithms through an extensive simulation experiments in terms of access cost, network traffic and locality access to objects.

Relay stations can be deployed in a wireless network to extend its coverage and improve its capacity. In this paper, we study a scheduling problem in OFDMA-based wireless relay networks with consideration for multi-user diversity, channel diversity and spatial reuse. First, we present a Mixed Integer Linear Programming (MILP) formulation to provide optimum solutions. It has been shown by previous research that performance of a wireless scheduling algorithm is usually related to the interference degree delta, which is the maximum number of links that interfere with a common link but do not interfere with each other. Therefore, we then show that the interference degree delta is at most 4 for any 2-hop relay network and 14 for any general h-hop (h >; 1) relay network. Furthermore, we present a simple greedy algorithm for the scheduling problem and show it has an approximation ratio of 1/(1+δ), which leads to an approximation ratio of 1/5 for the 2-hop case and 1/15} for the general case. In addition, we present three heuristic algorithms, namely, the weighted degree greedy algorithm, the Maximum Weighted Independent Set (MWIS) algorithm and the Linear Programming (LP) rounding algorithm, to solve the scheduling problem. Extensive simulation results have showed that the LP rounding algorithm performs best and always provides close-to-optimum solutions. The performance of the simple greedy algorithm is comparable to that of the other algorithms.

Efficient operation of wireless networks and switches requires using simple (and in some cases distributed) scheduling algorithms. In general, simple greedy algorithms (known as Greedy Maximal Scheduling - GMS) are guaranteed to achieve only a fraction of the maximum possible throughput (e.g., 50% throughput in switches). However, it was recently shown that in networks in which the Local Pooling conditions are satisfied, GMS achieves 100% throughput. Moreover, in networks in which the σ- Local Pooling conditions hold, GMS achieves σ% throughput. In this paper, we focus on identifying the specific network topologies that satisfy these conditions. In particular, we provide the first characterization of all the network graphs in which Local Pooling holds under primary interference constraints (in these networks GMS achieves 100% throughput). This leads to a polynomial time algorithm for identifying Local Pooling-satisfying graphs. Moreover, by using similar graph theoretical methods, we show that in all bipartite graphs (i.e., input-queued switches) of size up to 7×n, GMS is guaranteed to achieve 66% throughput, thereby improving upon the previously known 50% lower bound. Finally, we study the performance of GMS in interference graphs and show that in certain specific topologies its performance could be very bad. Overall, the paper demonstrates that using graph theoretical techniques can significantly contribute to our understanding of greedy scheduling algorithms.

This dissertation presents novel learning and optimization frameworks for sparse sensor scheduling in large-scale complex networks. In the first part, efficient algorithms for sensor scheduling in dynamical networks are introduced, with guaranteed performance. In the second part, the applications of these frameworks are explored, focusing on experimental design for nonlinear biological models and visual feature selection for robotic navigation. The first framework addresses sensor scheduling in discrete-time, linear time-invariant systems, proposing a novel learning-based rounding method to transform weighted sensor schedules into sparse, unweighted schedules, while preserving similar observability performance. The second framework extends this approach to linear time-varying systems, employing a myopic strategy within a Kalman filtering framework to address non-submodular sensor scheduling in large-scale Discrete-Time Linear Time-Varying (DT-LTV) systems. A simple greedy algorithm is utilized, providing approximation bounds based on submodularity and curvature concepts. The third framework explores a non-myopic approach for DT-LTV systems through an online sparse sensor scheduling methodology, leveraging randomized algorithms to approximate fully-sensed systems with a constant average number of active sensors at each time step. Finally, a non-myopic approach within a Kalman filtering framework is considered for DT-LTV dynamics, incorporating both process and measurement noise. This approach utilizes recent advances in online learning and regret minimization to offer an adaptive sensor scheduling framework, effectively addressing submodular objectives. In the second part of this dissertation, the focus shifts to the application of these frameworks, specifically addressing the challenge of selecting an optimal subset of observations to improve parameter estimation, a common problem in machine learning and signal processing. For nonlinear measurement models, we go beyond standard linear Taylor approximations by adopting a quadratic approximation for greater accuracy in highly nonlinear cases. An efficient greedy selection method with theoretical utility bounds is proposed to optimally select experiments, specifically demonstrated using the Michaelis-Menten model in a simple enzyme reaction system. In the final section, a task-oriented framework is developed to improve visual-inertial navigation in robots, addressing constraints such as time and energy. The framework selects visual landmarks using a mean squared error based, non-submodular objective and a simplified dynamic model. To solve the NP-hard landmark selection problem, three efficient algorithms are proposed: a simple greedy method, a randomized variant for faster results, and a Taylor series-based approximation. The greedy and randomized variant approaches provide performance guarantees with respect to the optimal solution. Simulation results conducted for each proposed framework validate the effectiveness and superiority of these methods compared to existing techniques. Additionally, potential future research directions are discussed in the conclusion.--Author's abstract

Influence maximization problem is to find a small set of influential nodes in a social network, whose activation of information propagation can be maximized using one of the propagation models such as independent cascade model. This paper proposes a new method to solve this problem based on discretized linear automaton algorithm and simple greedy algorithm. Every allowable node in the social network is regarded as an action and the goal of the learning automaton is to select an optimal subset of actions. To speed up the convergence, firstly, the problem space is reduced by excluding the nodes lacking influence; then, the original learning process is divided into two parts: the sampling process and the learning process. Besides, a new scheme for determining the best parameters is presented, which is more applicable to practical problems. The obtained results show that the new proposed algorithm is efficient in real-life social networks. The results are close to the ones obtained by the greedy algorithm in terms of accuracy, and the new method greatly improves the speed of selecting the optimal subset.

A coin set is a strictly increasing list of positive integers that always begins with 1. A coin set is called greedy when the simple greedy change-making algorithm always produces the fewest number of coins in change. Here, the greedy change-making algorithm repeatedly selects the largest denomination coin less than the remaining amount until it has assembled the correct change. Pearson has provided an efficient algorithm for determining whether a coin set is greedy. We study a stricter property on coin sets, called total greediness, which requires that all initial subsequences of the coin set also be greedy, and a simple property makes it easy to test if a coin set is totally greedy. We begin to explore the theory of greedy obstructions– those coin sets that cannot be extended to greedy coin sets by the addition of coins in larger denominations.

We study mechanisms for the combinatorial auction (CA) problem, in which m objects are sold to rational agents and the goal is to maximize social welfare. Of particular interest is the special case of s -CAs, where agents are interested in sets of size at most s , for which a simple greedy algorithm obtains an s + 1 approximation, but no polynomial time deterministic truthful mechanism is known to attain an approximation ratio better than O ( m /√log m ). We view this not only as an extreme gap between the power of greedy auctions and truthful greedy auctions, but also as exemplifying the gap between the known power of truthful and non-truthful polynomial time deterministic algorithms. We associate the notion of greediness with a broad class of algorithms, known as priority algorithms, which encapsulate many natural auction methods. This motivates us to ask: how well can a truthful greedy algorithm approximate the optimal social welfare for CA problems? We show that no truthful greedy priority algorithm can obtain an approximation to the CA problem that is sublinear in m , even for s -CAs with s ≥ 2. Our inapproximations are independent of any time constraints on the mechanism and are purely a consequence of the greedy-type restriction. We conclude that any truthful combinatorial auction mechanism with a non-trivial approximation factor must fall outside the scope of many natural auction methods.

In recent years, researchers in statistics and the UAI community have developed an impressive body of theory and algorithmic machinery for learning Bayesian networks from data. Learned Bayesian networks can be used for pattern discovery, prediction, diagnosis, and density estimation tasks. Early pioneering work in this area includes [5, 9, 10, 13]. The algorithm that has emerged as the current most popular approach is a simple greedy hill-climbing algorithm that searches the space of candidate structures, guided by a network scoring function (either Bayesian or Minimum Description Length (MDL)-based). The search begins with an initial candidate network (typically the empty network, which has no edges), and then considers making small local changes such as adding, deleting, or reversing an edge in the network.

Optimising city bus transport operations helps conserve fuel by providing the urban transport service as efficiently as possible. This study develops a Cloud-based Decision Support System (C-DSS) for transport analytics. The C-DSS is based on an intelligent model on location of depots for opening new depots and/or closing a few existing depots and allocation of city-buses to depots. The C-DSS is built on the Cloud Computing architecture with three layers and includes an efficient and simple greedy heuristic algorithm. Using modern information and communications technology tools, the proposed C-DSS minimizes the cost of city bus transport operations and in turn to reduce fuel consumption and CO2 emissions in urban passenger transport. The proposed C-DSS is demonstrated for its workability and evaluated for its performance on 25 large scale pseudo data generated based on the observation from Bangalore Metropolitan Transport Corporation (BMTC) in India.

A central question in information theory is to determine the maximum success probability that can be achieved in sending a fixed number of messages over a noisy channel. This was first studied in the pioneering work of Shannon who established a simple expression characterizing this quantity in the limit of multiple independent uses of the channel. Here we consider the general setting with only one use of the channel. We observe that the maximum success probability can be expressed as the maximum value of a submodular function. Using this connection, we establish the following results: 1. There is a simple greedy polynomial-time algorithm that computes a code achieving a (1-1/e)-approximation of the maximum success probability. Moreover, for this problem it is NP-hard to obtain an approximation ratio strictly better than (1-1/e). 2. Shared quantum entanglement between the sender and the receiver can increase the success probability by a factor of at most 1/(1-1/e). In addition, this factor is tight if one allows an arbitrary non-signaling box between the sender and the receiver. 3. We give tight bounds on the one-shot performance of the meta-converse of Polyanskiy-Poor-Verdu.

It is critical to design energy-efficient routing protocols for battery-limited mobile ad hoc networks, especially in which the energy-consuming MIMO techniques are employed. However, there are several challenges in such a design: first, it is difficult to characterize the energy consumption of a MIMO-based link; second, without a careful design, the broadcasted RREP packets, which are used in most energy-efficient routing protocols, could flood over the networks, and the destination node cannot decide when to reply the communication request; third, due to node mobility and persistent channel degradation, the selected route paths would break down frequently and hence the protocol overhead is increased further. To address these issues, in this paper, a novel Greedy Energy-Efficient Routing (GEER) protocol is proposed: (a) a generalized energy consumption model for the MIMO-based link, considering the trade-off between multiplexing and diversity gains, is derived to minimize link energy consumption and obtain the optimal transmit model; (b) a simple greedy route discovery algorithm and a novel adaptive reply strategy are adopted to speed up path setup with a reduced establishment overhead; (c) a lightweight route maintenance mechanism is introduced to adaptively rebuild the broken links. Extensive simulation results show that, in comparison with the conventional solutions, the proposed GEER protocol can significantly reduce the energy consumption by up to 68.74%.

Estimation of black-box functions often requires evaluating an extensive number of expensive noisy points. Learning algorithms can actively compare the similarity between the evaluated and unevaluated points to determine the most informative subsequent points for efficient estimation of expensive functions in a sequential procedure. In this paper, we propose an active learning methodology based on the integration of Laplacian regularization and active learning - Cohn (ALC) measure for identification of the most informative points for efficient estimation of noisy black-box functions using Gaussian processes. We propose two simple greedy search algorithms for sequential optimization of the tuning parameters and determination of subsequent points based on the information from the previously evaluated points. We also enhance the graph Laplacian with the information of both the predictor and response variables to capture the similarity between the points more effectively. The proposed methodology is particularly suited for problems involving estimation of expensive black-box functions with a high level of noise and plenty of unevaluated points. Using a case study for analysis of the kinematics of pitching in baseball as well as simulation experiments, we demonstrate the performance of the proposed methodology against existing methods in the literature in terms of estimation error.

In a Stackelberg pricing game a leader aims to set prices on a subset of a given collection of items, such as to maximize her revenue from a follower purchasing a feasible subset of the items. We focus on the case of computationally bounded followers who cannot optimize exactly over the range of all feasible subsets, but apply some publicly known algorithm to determine the set of items to purchase. This corresponds to general multi-dimensional pricing assuming that consumers cannot optimize over the full domain of their valuation functions but still aim to act rationally to the best of their ability.We consider two versions of this novel type of Stackelberg pricing games. Assuming that items are weighted objects and the follower seeks to purchase a min-cost selection of objects of some minimum weight (the Min-Knapsack problem) and uses a simple greedy 2-approximate algorithm, we show how an extension of the known single-price algorithm can be used to derive a polynomial-time (2 + ε)-approximation algorithm for the leader’s revenue maximization problem based on so-called near-uniform price assignments. We also prove the problem to be strongly NP-hard.Considering the case that items are subsets of some ground set which the follower seeks to cover (the Set-Cover problem) via a standard primal-dual approach, we prove that near-uniform price assignments fail to yield a good approximation guarantee. However, in the special case of elements with frequency 2 (the Vertex-Cover problem) it turns out that exact revenue maximization can be done in polynomial-time. This stands in sharp contrast to the fact that revenue maximization becomes APX-hard already for elements with frequency 3.KeywordsGreedy AlgorithmVertex CoverPrice ProblemCongestion GameApproximation GuaranteeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Image search re-ranking has proven its effectiveness in the text-based image search system. However, traditional re-ranking algorithm heavily relies on the relevance of the top-ranked images. Due to the huge semantic gap between query and the image, the text-based retrieval result is unsatisfactory. Besides, single re-ranking model has large variance and is easy to over-fit. Instead, multiple re-ranking models can better balance the biased and the variance. In this paper, we first conduct label de-noising to filter false-positive images. Then a simple greedy graph-based re-ranking algorithm is proposed to derive the resulting list. Afterwards, different images are chosen as the seed images to perform re-ranking multiple times. Using the rank fusion, the results from different graphs are combined to form a better result. Extensive experiments are conducted on the INRIA web353 dataset and demonstrate that our method achieves significant improvement over state-of-the-art methods.