Round Algorithm Research Articles

Energy-efficient resource block assignment and power control for underlay device-to-device communications in multi-cell networks

We propose an energy-efficient resource block (RB) assignment and power control strategy for underlay device-to-device (D2D) communications in multi-cell networks, where more than one D2D pair is allowed to share the same RBs with cellular user equipments (CUEs). We first formulate the problem as a nonconvex mixed-integer fractional programming problem, which is NP-hard, and then separate the problem into two subproblems, namely RB assignment and power control, to design a two-stage energy-efficient strategy with reasonable complexity. During the first stage, the RBs are assigned to CUEs by a sequential geometric programming (SGP) algorithm and a rate-based round algorithm, while during the second stage, the power control strategy for CUEs and D2D pairs is designed using the SGP algorithm. Numerical simulations are conducted to examine the convergence behavior of our proposed strategy, as well as to evaluate the impact of system parameters on the performance of our proposed strategy.

Geometric rounding and feature separation in meshes

Geometric rounding of a 3D triangle mesh is the task of approximating the vertex coordinates by floating point numbers while preserving the topology. We present a practical geometric rounding algorithm based on a novel strategy: (1) modify the mesh to achieve a feature separation that prevents topology changes when the coordinates change by the rounding unit; and (2) round each vertex coordinate to the closest floating point number. The geometric rounding algorithm allows computational geometry algorithms to interface with numerical algorithms. Mesh feature separation is also useful on its own, for example for enforcing minimum feature sizes in CAD models. We demonstrate a robust, efficient implementation.

Minimal Cost Server Configuration for Meeting Time-Varying Resource Demands in Cloud Centers

We consider the minimal cost server configuration for meeting resource demands over multiple time slots. Specifically, there are some heterogeneous servers. Each server is specified by a cost, certain amounts of several resources, and an active interval, i.e., the time interval that the server is planed to work. There are different overall demands for each type of resource over different time slots. A feasible solution is a set of servers such that at any time slot, the resources provided by the selected servers are at least their corresponding demands. Notice that, a selected server can not provide resources for the time slots out of its active interval. The total cost of the solution is the summation of the costs of all selected servers. The goal is to find a feasible solution with minimal total cost. This problem is proved to be NP-hard due to a reduction from the multidimensional knapsack problem (MKP), which is a well-known NP-hard combinational optimization problem. To solve our problem, we present a randomized approximation algorithm called partial rounding algorithm ( $\mathcal {PRA}$ ), which guarantees $O\left(\log \left(KT \right) \right)$ -approximation, i.e., $\eta \;\log \left(KT \right)$ -approximation, where $K$ is the number of kinds of resources, $T$ is the number of time slots, and $\eta$ is a positive constant. Furthermore, to minimize $\eta$ as much as possible, we propose a varied Chernoff bound and apply it in $\mathcal {PRA}$ . We perform extensive experiments with random inputs and a specific application input. The results show that $\mathcal {PRA}$ with our varied Chernoff conclusion can find solutions closing to the optimal one.

Approximation Algorithms for Minimum-Load k -Facility Location

We consider a facility-location problem that abstracts settings where the cost of serving the clients assigned to a facility is incurred by the facility. Formally, we consider the minimum-load k-facility location (ML k FL) problem, which is defined as follows. We have a set F of facilities, a set C of clients, and an integer k ≥ 0. Assigning client j to a facility f incurs a connection cost d ( f , j ). The goal is to open a set F ⊆ F of k facilities and assign each client j to a facility f ( j )∈ F so as to minimize max f ∈ F ∑ j ∈ C : f ( j )= f d ( f , j ); we call ∑ j ∈ C : f ( j )= f d ( f , j ) the load of facility f . This problem was studied under the name of min-max star cover in References [3, 7], who (among other results) gave bicriteria approximation algorithms for ML k FL for when F = C . ML k FL is rather poorly understood, and only an O ( k )-approximation is currently known for ML k FL, even for line metrics . Our main result is the first polytime approximation scheme (PTAS) for ML k FL on line metrics (note that no non-trivial true approximation of any kind was known for this metric). Complementing this, we prove that ML k FL is strongly NP -hard on line metrics. We also devise a quasi-PTAS for ML k FL on tree metrics. ML k FL turns out to be surprisingly challenging even on line metrics and resilient to attack by a variety of techniques that have been successfully applied to facility-location problems. For instance, we show that (a) even a configuration-style LP-relaxation has a bad integrality gap and (b) a multi-swap k -median style local-search heuristic has a bad locality gap. Thus, we need to devise various novel techniques to attack ML k FL. Our PTAS for line metrics consists of two main ingredients. First, we prove that there always exists a near-optimal solution possessing some nice structural properties. A novel aspect of this proof is that we first move to a mixed-integer LP (MILP) encoding of the problem and argue that a MILP-solution minimizing a certain potential function possesses the desired structure and then use a rounding algorithm for the generalized-assignment problem to “transfer” this structure to the rounded integer solution. Complementing this, we show that these structural properties enable one to find such a structured solution via dynamic programming.

Performance Evaluation of SHA-3 Final Round Candidate Algorithms on ARM Cortex–M4 Processor

SHA-3 was an open competition initiated by NIST to design new generation of hash functions. This competition was a necessity to overcome the challenges imposed by multiple attacks on MDx family of hash functions including SHA-0 and SHA-1. For this competition, NIST announced a reference platform which did not cover Embedded and Mobile machines. This paper compares the performance of SHA-3 final round candidate algorithms on ARM Cortex-M4 processor (embedded processor) and presents the results. Cycles per Byte is used as performance metric. Cortex-M4 based Stellaris® LM4F232 Evaluation Board (EK-LM4F232) from Texas Instruments is used for performance evaluation.

Breaching Security of Full Round Tiny Encryption Algorithm

Tiny encryption algorithm is a 64-bit block cipher designed by Wheeler and Needham in 1994 and attracted much of its attention due to its capability of reducing the hardware cost. In this paper, we introduced coincidence count attack at bit level, a kind of known-plaintext attack and evaluated the resistance of TEA to withstand with it. We also examined confrontation of full round TEA against bit sum attack. Furthermore, we introduced a modest algorithm based on coincidence count and bit sum concept that makes it easy to find relevant plaintext corresponding to an arbitrary cipher text with a probability of 0.93. We also presented how cipher text originated from tiny encryption algorithm can be distinguished from a random permutation of binary sequence.

Spectrum Sharing for Heterogeneous Networks and Application Systems in TV White Spaces

In 2010, federal communications commission released the final ruling to allow the unlicensed operation of TV white spaces, i.e., locally vacant TV channels. Since TV white spaces are open to all networks and all types of applications, it is likely that there will be multiple networks and application systems authorized to use the same TV channels at the same time. Currently, there is mechanism for different users to operate in the TV white spaces within one system, while TV spectrum sharing among heterogeneous networks and application systems is largely ignored. To address the problem, this paper designs a trading mechanism to study the TV spectrum market between Geolocation database and heterogeneous application systems. We formulate the spectrum sharing problem into a 0–1 integer optimization problem and prove that this problem is NP-complete. The proposed solution decomposes an optimal fractional solution of a NP-hard problem into a convex combination of internal solutions by randomized rounding algorithm. Simulation results show that the proposed approximation algorithm can achieve a close-to-optimal solution with far less complexity.

Compact Hardware Implementations of MISTY1 Block Cipher

This paper proposes compact hardware implementations of 64-bit NESSIE proposed MISTY1 block cipher for area constrained and low power ASIC applications. The architectures comprise only one round MISTY1 block cipher algorithm having optimized FO/FI function by re-utilizing S9/S7 substitution functions. A focus is also made on efficient logic implementations of S9 and S7 substitution functions using common sub-expression elimination (CSE) and parallel AND/XOR gates hierarchy. The proposed architecture 1 generates extended key with independent FI function and is suitable for MISTY1 8-rounds implementation. On the other hand, the proposed architecture 2 uses a single FO/FI function for both MISTY1 round function as well as extended key generation and can be employed for MISTY1 [Formula: see text] rounds. To analyze the performance and covered area for ASICs, Synopsys Design Complier, SMIC 0.18[Formula: see text][Formula: see text]m @ 1.8[Formula: see text]V is used. The hardware constituted 3041 and 2331 NAND gates achieving throughput of 171 and 166 Mbps for 8 rounds implementation of architectures 1 and 2, respectively. Comprehensive analysis of proposed designs is covered in this paper.

Communication Steps for Parallel Query Processing

We study the problem of computing conjunctive queries over large databases on parallel architectures without shared storage. Using the structure of such a query q and the skew in the data, we study tradeoffs between the number of processors, the number of rounds of communication, and the per-processor load —the number of bits each processor can send or can receive in a single round—that are required to compute q . Since each processor must store its received bits, the load is at most the number of bits of storage per processor. When the data are free of skew, we obtain essentially tight upper and lower bounds for one round algorithms, and we show how the bounds degrade when there is skew in the data. In the case of skewed data, we show how to improve the algorithms when approximate degrees of the (necessarily small number of) heavy-hitter elements are available, obtaining essentially optimal algorithms for queries such as skewed simple joins and skewed triangle join queries. For queries that we identify as treelike , we also prove nearly matching upper and lower bounds for multi-round algorithms for a natural class of skew-free databases. One consequence of these latter lower bounds is that for any ε > 0, using p processors to compute the connected components of a graph, or to output the path, if any, between a specified pair of vertices of a graph with m edges and per-processor load that is O ( m / p 1−ε ) requires Ω(log p ) rounds of communication. Our upper bounds are given by simple structured algorithms using MapReduce. Our one-round lower bounds are proved in a very general model, which we call the Massively Parallel Communication (MPC) model, that allows processors to communicate arbitrary bits. Our multi-round lower bounds apply in a restricted version of the MPC model in which processors in subsequent rounds after the first communication round are only allowed to send tuples.

Decision tree classification with bounded number of errors

Oblivious decision trees are decision trees where every node in the same level is associated with the same attribute. These trees have been studied in the context of feature selection.In this paper, we study the problem of constructing an oblivious decision tree that incurs at most k classification errors, where k is a given integer. We present a randomized rounding algorithm that, given a parameter 0<ϵ<1/2, builds an oblivious decision tree with cost at most (3/(1−2ϵ))ln⁡(n)OPT(I) and produces at most (k/ϵ) errors, where OPT(I) is the optimal cost and n is the number of objects. The probability of failure of this algorithm is at most (n−1)/2n2. The logarithmic factor in the cost of the tree is the best possible attainable, even for k=0, unless P=NP.

Approximating min-cost chain-constrained spanning trees: a reduction from weighted to unweighted problems

We study the min-cost chain-constrained spanning-tree (MCCST) problem: find a min-cost spanning tree in a graph subject to degree constraints on a nested family of node sets. We devise the first polytime algorithm that finds a spanning tree that (i) violates the degree constraints by at most a constant factor and (ii) whose cost is within a constant factor of the optimum. Previously, only an algorithm for unweighted CCST was known (Olver and Zenklusen in Proceedings of the 16th IPCO, pp 324–335, 2013), which satisfied (i) but did not yield any cost bounds. This also yields the first result that obtains an O(1)-factor for both the cost approximation and violation of degree constraints for any spanning-tree problem with general degree bounds on node sets, where an edge participates in a super-constant number of degree constraints. A notable feature of our algorithm is that we reduce MCCST to unweighted CCST (and then utilize Olver and Zenklusen in Proceedings of the 16th IPCO, pp 324–335, 2013) via a novel application of Lagrangian duality to simplify the cost structure of the underlying problem and obtain a decomposition into certain uniform-cost subproblems. We show that this Lagrangian-relaxation based idea is in fact applicable more generally and, for any cost-minimization problem with packing side-constraints, yields a reduction from the weighted to the unweighted problem. We believe that this reduction is of independent interest. As another application of our technique, we consider the k -budgeted matroid basis problem, where we build upon a recent rounding algorithm of Bansal and Nagarajan (Proceedings of IPCO 2016. arXiv:1512.02254 , 2015) to obtain an improved $$n^{O(k^{1.5}/\epsilon )}$$ -time algorithm that returns a solution that satisfies (any) one of the budget constraints exactly and incurs a $$(1+\epsilon )$$ -violation of the other budget constraints.

An Improved Algorithm for Fixed-Hub Single Allocation Problems

This paper discusses the fixed-hub single allocation problem (FHSAP). In this problem, a network consists of hub nodes and terminal nodes. Hubs are fixed and fully connected; each terminal node is assigned to a single hub which routes all its traffic. The goal is to minimize the cost of routing the traffic in the network. In this paper, we propose a new linear programming (LP) relaxation for this problem by incorporating a set of validity constraints into the classical formulations by Ernst and Krishnamoorthy (Locat Sci 4:139–154, Ann Op Res 86:141–159). A geometric rounding algorithm is then used to obtain an integral solution from the fractional solution. We show that by incorporating the validity constraints, the strengthened LP often provides much tighter upper bounds than the previous methods with a little more computational effort and the solution obtained often has a much smaller gap with the optimal solution. We also formulate a robust version of the FHSAP and show that it can guard against data uncertainty with little costs.

A modified weighted round robin scheduling algorithm in TTE

A modified weighted round robin scheduling algorithm in TTE

Resource Allocation for D2D Communication Underlaid Cellular Networks Using Graph-Based Approach

In this paper, we study the non-orthogonal dynamic spectrum sharing for device-to-device (D2D) communications in the D2D underlaid cellular network. Our design aims to maximize the weighted system sum-rate under the constraints that: 1) each cellular or active D2D link is assigned one subband and 2) the required minimum rates for cellular and active D2D links are guaranteed. To solve this problem, we first characterize the optimal power allocation solution for a given subband assignment. Based on this result, we formulate the subband assignment problem by using the graph-based approach, in which each link corresponds to a vertex and each subband assignment is represented by a hyper-edge. We then propose an iterative rounding algorithm and an optimal branch-and-bound (BnB) algorithm to solve the resulting graph-based problem. We prove that the iterative rounding algorithm achieves at least 1/2 of the optimal weighted sum-rate. Extensive numerical studies illustrate that the proposed iterative rounding algorithm significantly outperforms the conventional spectrum sharing algorithms and attains almost the same system sum-rate as the optimal BnB algorithm.

Optimal Mechanisms for Combinatorial Auctions and Combinatorial Public Projects via Convex Rounding

We design the first truthful-in-expectation, constant-factor approximation mechanisms for NP -hard cases of the welfare maximization problem in combinatorial auctions with nonidentical items and in combinatorial public projects. Our results apply to bidders with valuations that are nonnegative linear combinations of gross-substitute valuations, a class that encompasses many of the most well-studied subclasses of submodular functions, including coverage functions and weighted matroid rank functions. Our mechanisms have an expected polynomial runtime and achieve an approximation factor of 1 − 1/ e . This approximation factor is the best possible for both problems, even for known and explicitly given coverage valuations, assuming P ≠ NP . Recent impossibility results suggest that our results cannot be extended to a significantly larger valuation class. Both of our mechanisms are instantiations of a new framework for designing approximation mechanisms based on randomized rounding algorithms. The high-level idea of this framework is to optimize directly over the (random) output of the rounding algorithm , rather than the usual (and rarely truthful) approach of optimizing over the input to the rounding algorithm. This framework yields truthful-in-expectation mechanisms, which can be implemented efficiently when the corresponding objective function is concave. For bidders with valuations in the cone generated by gross-substitute valuations, we give novel randomized rounding algorithms that lead to both a concave objective function and a (1 − 1/ e )-approximation of the optimal welfare.

Energy-Efficient Resource Allocation for D2D Communications in Cellular Networks

In this paper, we study the energy-efficient resource allocation problem for device-to-device (D2D) communication underlaying cellular networks, which aims to maximize the minimum weighted energy efficiency of D2D links while guaranteeing minimum data rates for cellular links. We first characterize the optimal power allocation of the cellular links to transform the original resource allocation problem into the joint subchannel and power allocation problem for D2D links. We then propose three resource allocation algorithms with different complexity levels, namely, dual-based, branch-and-bound (BnB), and relaxation-based rounding (RBR) algorithms. While the dual-based algorithm solves the problem by using the dual decomposition method, the BnB and RBR algorithms tackle the problem by employing the relaxation approach. We establish the strong performance guarantees for the proposed algorithms through theoretical analysis. Extensive numerical studies demonstrate that the proposed algorithms achieve superior performance and significantly outperform a conventional algorithm.

Energy-efficient contention-aware application mapping and scheduling on NoC-based MPSoCs

We consider the problem of energy-efficient contention-aware application mapping and scheduling on Network-on-Chip (NoC) based multiprocessors. For an application represented by a directed acyclic graph, we present a model where voltage scaling techniques for processors can be combined with frequency tuning techniques for NoC links to save overall system energy consumption. We employ a two-step approach to solve the overall mapping and scheduling problem. First, the application mapping problem is formulated as a quadratic binary programming problem, which aims to minimize the communication energy; we apply a relaxation-based iterative rounding algorithm to solve it. With the mapping achieved, we further consider the application scheduling problem, which aims to find the optimal voltage level for each task of the application and optimal frequency level for each communication of the application to minimize the overall system energy consumption, given the application deadline. To attack the second problem, we first design an algorithm based on the earliest time first scheduling to determine the application’s finish time if a voltage and frequency assignment is given; then, we develop a genetic algorithm to search the solution space for the voltage and frequency assignment that minimizes the overall system energy consumption and meets the application’s deadline. Through these two steps, we produce a mapping and scheduling that meets the application’s deadline, and significantly reduces the overall system energy consumption. Experiments are conducted for a number of randomly generated application graphs, as well as several real application graphs to verify the energy reduction and applicability of the proposed model and algorithms.

Erratum: Two-Level QTT-Tucker Format for Optimized Tensor Calculus

We prove by counterexample that the bound on the rounding error given in Theorem 5.2 of [Dolgov and Khoromskij, SIAM J. Matrix Anal. Appl., 34 (2013), pp. 593--623] does not hold in general. A correct version of the error bound as well as a modified rounding algorithm for which the original bound holds are presented.

Optimal Association in Wireless Mesh Networks

The wireless multihop backhaul is a unique feature of wireless mesh networks (WMNs), which necessitates redesign of association control algorithms. In this paper, we formulate and propose approximation algorithms for the problem of optimal joint association and bandwidth allocation in WMNs, considering max–min fairness (MM) and proportional fairness (PF) objectives. We first relax the integral association constraint and get an optimal fractional association solution. Then, we propose two rounding algorithms, namely, largest fraction rounding and bipartite graph rounding, to get an integral solution and analyze their theoretical approximation ratios. Finally, we propose two approximation ratio improvement algorithms so that the improved approximation ratio can more accurately reflect the true performance gap between the produced solution and the optimal one. Our simulation results show that the proposed algorithms achieve performance that is close to the optimal and outperform popular heuristic algorithms. We also compare the performance of PF and MM in WMNs in terms of network throughput and fairness in user bandwidth. Finally, we compare the performances of the proposed rounding algorithms and show that the approximation ratio can be reduced to 1–2 by the proposed ratio improvement algorithms. Therefore, our proposed algorithm is able to achieve nearly optimal association control, as well as bandwidth allocation, considering MM or PF, with small approximation ratios, in WMNs.

A QOS Based Load Balanced Switch

The simple architecture with high forwarding capacity bandwidth is load balancing switch is build with two stage switch fabric to eliminate the mis sequencing problems and kept packets of the same flow in the order of load balanced two stage switch. Before load balancing two stages has perform with the Full frame first algorithm and use centralized scheduler to eliminate those mis sequencing problemsand getting the 100% throughput result. There comes at some additional cost and needs costly online scheduling algorithms and need for a complex scheduler and quality being reduced. In this paper we introduce the two stage switch fabric with round robin scheduling algorithmis used to solve mis sequencing problems and two maximum weight matching algorithms Longest queue first(LQF) and Oldest cell first(OCF) to achieve 100% throughput results. Theoretical analysis and simulation results shows that using these algorithms, achieve all the possible outcome results in the switch. � The simple architecture with the load balancing scheme perform with interesting two different stage switch fabric to eliminate the mis sequencing problems and kept packets of the same flow to the destination path in the order of load balanced two stage switch fabric. The two stage load balancing switch is more scalable than the any other switch in the network architecture. Hardly load balanced switch got some problem with that, on sending and receiving the data in wired or wireless networks(8), the major problem with that is mis sequencing problems has arised to loss of data packets or mis matched data formats. Somehow in earlier they are tired to clear those problems with the algorithms named, Full frame first algorithm to get mis sequencing problems and they put the centralized schedular to achieve the 100% throughput results(4)(2) in their data packets.Oftenly they got the perfect data packets arrival in destination, but the problem with that methodology is the quality of data is reduced to lower. And manually they they need costly online scheduling algorithms to rectify the mis matching of data and need more complex schedular to achieve the 100% throughput result of outcome data. We introduce in this paper to rectify the mis sequencing problems(1) and avoid the costly online scheduling algorithms, we use Round robin scheduling algorithms(RRS) to rectify the mis matching of data packets in the tcp applications and two maximum weight matching algorithms namely, Longest queue first(LOQ) and Oldest cell first(OCF) to achieve 100% throughput result for all independent arrival packets.(11)These algorithms are used to eliminate the complex schedular and needs of online costly scheduling algorithm to schedule the data packets in the destination node. The another approach of this proposed is to get the high quality of data packets in destination node which is the data which is send by sender, the receiver also got the same quality of data(9) without defragmentation and reduction of quality. We observed that in the algorithms and methodolgy of using those above like, RRS, LOQ and OCF, not only to solve mis sequencing problems and also get quality of data packets service of the same aaplication(10). Yet we are consider more algorithm to get the quality of data packets. Our idea is to just keep packets