14773410
Algorithmic aspects of capacity in wireless networks
This paper considers two inter-related questions: (i) Given a wireless ad-hoc network and a collection of source-destination pairs {(si,ti)}, what is the maximum throughput capacity of the network, i.e. the rate at which data from the sources to their corresponding destinations can be transferred in the network? (ii) Can network protocols be designed that jointly route the packets and schedule transmissions at rates close to the maximum throughput capacity? Much of the earlier work focused on random instances and proved analytical lower and upper bounds on the maximum throughput capacity. Here, in contrast, we consider arbitrary wireless networks. Further, we study the algorithmic aspects of the above questions: the goal is to design provably good algorithms for arbitrary instances. We develop analytical performance evaluation models and distributed algorithms for routing and scheduling which incorporate fairness, energy and dilation (path-length) requirements and provide a unified framework for utilizing the network close to its maximum throughput capacity.Motivated by certain popular wireless protocols used in practice, we also explore "shortest-path like" path selection strategies which maximize the network throughput. The theoretical results naturally suggest an interesting class of congestion aware link metrics which can be directly plugged into several existing routing protocols such as AODV, DSR, etc. We complement the theoretical analysis with extensive simulations. The results indicate that routes obtained using our congestion aware link metrics consistently yield higher throughput than hop-count based shortest path metrics.
16314241
End-to-end packet-scheduling in wireless ad-hoc networks
Packet-scheduling is a particular challenge in wireless networks due to interference from nearby transmissions. A distance-2 interference model serves as a useful abstraction here, and we study packet routing and scheduling under this model. The main focus of our work is the development of fully-distributed (decentralized) protocols. We present polylogarithmic/constant factor approximation algorithms for various families of disk graphs (which capture the geometric nature of wireless-signal propagation), as well as near-optimal approximation algorithms for general graphs. The packet-scheduling work by L eighton, Maggs and Rao (Combinatorica, 1994) and a basic distributed coloring procedure, originally due to Luby (J. Computer and System Sciences, 1993), underlie many of our algorithms. Experimental work of Finocchi, Panconesi, and Silvestri (SODA 2002) showed that a natural modification of Luby's algorithm leads to improved performance, and a rigorous explanation of this was left as an open question; we prove that the modified algorithm is provably better in the worst-case. Finally, using simulations, we study the impact of the routing strategy and the choice of parameters on the performance of our distributed algorithm for unit disk graphs.
5564142
Provable algorithms for parallel generalized sweep scheduling
Abstract We present provably efficient parallel algorithms for sweep scheduling, which is a commonly used technique in radiation transport problems, and involves inverting an operator by iteratively sweeping across a mesh from multiple directions. Each sweep involves solving the operator locally at each cell. However, each direction induces a partial order in which this computation can proceed. On a distributed computing system, the goal is to schedule the computation, so that the length of the schedule is minimized. Due to efficiency and coupling considerations, we have an additional constraint, namely, a mesh cell must be processed on the same processor along each direction. Problems similar in nature to sweep scheduling arise in several other applications, and here we formulate a combinatorial generalization of this problem that captures the sweep scheduling constraints,and call it the generalized sweep scheduling problem. Several heuristics have been proposed for this problem; see [S. Pautz, An algorithm for parallel S n sweeps on unstructured meshes, Nucl. Sci. Eng. 140 (2002) 111–136; S. Plimpton, B. Hendrickson, S. Burns, W. McLendon, Parallel algorithms for radiation transport on unstructured grids, Super Comput. (2001)] and the references therein; but none of these have provable worst case performance guarantees. Here we present a simple, almost linear time randomized algorithm for the generalized sweep scheduling problem that (provably) gives a schedule of length at most O ( log 2 n ) times the optimal schedule for instances with n cells, when the communication cost is not considered, and a slight variant, which coupled with a much more careful analysis, gives a schedule of (expected) length O ( log m log log log m ) times the optimal schedule for m processors. These are the first such provable guarantees for this problem. The algorithm can be extended with an additional multiplicative factor in the case when we have inter-processor communication latency, in the models of Rayward-Smith [UET scheduling with inter-processor communication delays, Discrete Appl. Math. 18 (1) (1987) 55–71] and Hwang et al. [Scheduling precedence graphs in systems with inter-processor communication times, SIAM J. Comput. 18(2) (1989) 244–257]. Our algorithms are extremely simple, and use no geometric information about the mesh; therefore, these techniques are likely to be applicable in more general settings. We also design a priority based list schedule using these ideas, with the same theoretical guarantee, but much better performance in practice; combining this algorithm with a simple block decomposition also lowers the overall communication cost significantly. Finally, we perform a detailed experimental analysis of our algorithm. Our results indicate that the algorithm compares favorably with the length of the schedule produced by other natural and efficient parallel algorithms proposed in the literature [S. Pautz, An Algorithm for parallel S n sweeps on unstructured meshes, Nucl. Sci. Eng. 140 (2002) 111–136; S. Plimpton, B. Hendrickson, S. Burns, W. McLendon, Parallel algorithms for radiation transport on unstructured grids, Super Comput. (2001)].
38425944
Scheduling on Unrelated Machines Under Tree-Like Precedence Constraints
We present polylogarithmic approximations for the R|prec|Cmax and R|prec|∑jwjCj problems, when the precedence constraints are “treelike” – i.e., when the undirected graph underlying the precedences is a forest. We also obtain improved bounds for the weighted completion time and flow time for the case of chains with restricted assignment – this generalizes the job shop problem to these objective functions. We use the same lower bound of “congestion+dilation”, as in other job shop scheduling approaches. The first step in our algorithm for the R|prec|Cmax problem with treelike precedences involves using the algorithm of Lenstra, Shmoys and Tardos to obtain a processor assignment with the congestion + dilation value within a constant factor of the optimal. We then show how to generalize the random delays technique of Leighton, Maggs and Rao to the case of trees. For the weighted completion time, we show a certain type of reduction to the makespan problem, which dovetails well with the lower bound we employ for the makespan problem. For the special case of chains, we show a dependent rounding technique which leads to improved bounds on the weighted completion time and new bicriteria bounds for the flow time.
6168494
Approximation algorithms for scheduling on multiple machines
We develop a single rounding algorithm for scheduling on unrelated parallel machines; this algorithm works well with the known linear programming, quadratic programming, and convex programming-relaxations for scheduling to minimize completion time, makespan, and other well-studied objective functions. We obtain the following applications for the general setting of unrelated parallel machines: (i) a bicriteria algorithm for a schedule whose weighted completion-time and makespan simultaneously exhibit the current-best individual approximations for these criteria (3/2 and 2, respectively); (ii) better-than-two approximation guarantees for scheduling under the L/sub p/ norm for all 1 < p < /spl infin/, improving on the 2-approximation algorithms of Azar & Epstein; and (iii) the first constant-factor multicriteria approximation algorithms that handle the weighted completion-time and any given collection of integer L/sub p/ norms. Our algorithm yields a common generalization of rounding theorems due to Karp et al and Shmoys & Tardos; among other applications, this yields an improved approximation for scheduling with resource-dependent processing times studied by Grigoriev et al.
15533433
Explicit dispersers with polylog degree
An (N, M, ‘T)-disperser is a duected bipartite Multigraph G = (V, W,E) with IV[ = N, IW[ = M and all edges directed from V to W, having the following expansion property: any subset of V having at least T vertices has a neighbor set of sise at least M/2. For any pair of constants (, ~, 1 z ~ > ~ z 0, ~y suffiaently large N, and for any T ~ 2(106@, M < 2(I%N)A , we give an explicit elementary construction ~f an (N, M, T)-disperser such that the out-degree of any vertex in V is at most polylogarithmic in N. Using this with known applications of dispersers yields several results. First, our construction implies that the complexity class Strong-RP defined by Sipser, equals RP. Second, for arty fixed q > 0, we give the first polynomial-time simulation of RP algorithms using the output of any “minimally randomn source. For any integral R >0, such a source accepts a single request for an R-bit string and generates the string according to a distribution that assigns probahiity at most 2-R’ to any string. It is minimally random in the sense that any weaker source is insufficient to do a blackbox polynomial-time simulation of RP algorithms. Third, we show improvements on the expander construction and the consequent applications given by Wlgderson and Zuck“The full version of thk work will be available at the DIMACS www site soon (URIJ http:ildirnacs. r-utgers. edu). The first and third authors were supported in part by NSF grant CCR-92 15293. The secoud author was supported in part by grant 93-6-6 of the Alfred P. Sloan Foundation to the Institute for Advanced Study, and in part by ESPRIT Bcsic Research Action Programme of the EC under contract No. 7141 (project ALCOM II). All three authors were also supported in part by DIMACS (Center for Discrete Mathematics & Theoretical Computer Science), through NSF grant NSF-STC91-19999 and by the New Jersey Commission on Science and Technology. *Dep~ment of Mathematics, Rutgem University, New Brunswick, NJ 08854, USA. Email: saka@math.ntgers. edn. $ school of Mathematics, Institute for Advanced Study, prince ton, NJ 08540, USA. Parts of this work were done while at DIMACS, while visiting the Department of Applied Mathematics and Computer Science, \Veizmann Institute of Science, Rehovot 76100, Israel, and while visiting the Department of Computer Science, University of Warwick, Coventry CV4 7AL, UK. Email: aravind@dca.warwick. ac.uk. SrJep~ment of Computer Science, Rutgers University, New Brunswick, NJ 08854, USA. Email: szhou@cs. rutgers. edu. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyri ht notice and the 3 title of the publication and. tis date appear,. an notice is given that copym IS by pernws~n of the Asscqatlon of Computing Machinery. o cop otherwe, or to repubkh, requires ‘{ a fee ancVor spec m permissmn. STOC’ 95, Las Vegas, Nevada, USA O 1995 ACM 0-89791 -718-9195/0005 ..$3.50 erman. Applying our disperser to a reduction due to Zuckerman, we show that approximating log log u(G) (where w(G) denotes the maximum clique sise of a given graph G) to within any constant tkctor cannot be done in deterministic quaei-polynomial time, assuming that rion-deterministic quasbpolynomial time does not equal deterministic quaaipolynomial time. Finally, we improve knolwn results due to Fiat and Naor and Zuckerman, for a problem in data structures: implicit 0(1 ) probe search.
18206354
Optimal design of signaling networks for Internet telephony
We present an approach for efficient design of a signaling network for a network of software switches supporting Internet telephony. While one may take an integer programming approach to solve this problem, it quickly becomes intractable even for modest-sized networks. Instead, our topology design uses random graphs that we show to be nearly optimal in cost, highly connected, and computationally efficient even for large networks. We then formulate a quadratic assignment problem (QAP) to map the abstract topology into the physical network to achieve optimal load balancing for given demand forecasts, which we solve using randomized heuristics. Numerical results on several example networks illustrate the performance and computational efficiency of our method. A graphical design tool has been developed based on our algorithms.
11919636
Quick-release fair scheduling
In prior work on multiprocessor fairness, efficient techniques with provable properties for reallocating spare processing capacity have been elusive. In this paper, we address this shortcoming by proposing a new notion of multiprocessor fairness, called quick-release fair (QRfair) scheduling. Under QRfair scheduling, each task is specified by giving both a minimum and a maximum weight (i.e., processor share). The goal is to schedule each task (as the spare capacity changes) at a rate that is (i) at least that implied by its minimum weight and (ii) at most that implied by its maximum weight. We present a quick-release variant of the PD/sup 2/ Pfair scheduling algorithm called PD/sup Q/ and prove that the allocations of PD/sup Q/ always satisfy (i) and (ii). Also, we present results from simulation experiments that show the efficacy of PD/sup Q/.
14860992
Scalable Time-Parallelization of Molecular Dynamics Simulations in Nano Mechanics
Molecular dynamics (MD) is an important atomistic simulation technique, with widespread use in computational chemistry, biology, and materials. An important limitation of MD is that the time step size is small, requiring a large number of iterations to simulate realistic time spans. Conventional parallelization is not very effective for this. We recently introduced a new approach to parallelization, where data from related prior simulations are used to parallelize a new computation along the time domain. In our prior work, the size of the physical system in the current simulation needed to be identical to that of the prior simulations. The significance of this paper lies in demonstrating a strategy that enables this approach to be used even when the physical systems differ in size. Furthermore, this method scaled up to almost 1000 processors with close to ideal speedup in one case, where conventional methods scale to only 2-3 processors
11533466
Edge Domination on Bipartite Permutation Graphs and Cotriangulated Graphs
An edge dominating set D of graph G = (V, E) is a set of edges such that every edge not in D is adjacent to at least one edge in D. We develop polynomial time algorithms for finding a minimum edge dominating set for a cotriangulated graph and a bipartite permutation graph.