Topic
Average-case complexity
About: Average-case complexity is a research topic. Over the lifetime, 1749 publications have been published within this topic receiving 44972 citations.
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TL;DR: This paper presents two optimization algorithms that solve the optimization problem of jointly selecting the best set of reference frames and their associated transport QoS levels in a multipath streaming setting globally optimally and locally optimally with lower complexity.
Abstract: Recent video coding standards such as H.264 offer the flexibility to select reference frames during motion estimation for predicted frames. In this paper, we study the optimization problem of jointly selecting the best set of reference frames and their associated transport QoS levels in a multipath streaming setting. The application of traditional Lagrangian techniques to this optimization problem suffers from either bounded worst case error but high complexity or low complexity but undetermined worst case error. Instead, we present two optimization algorithms that solve the problem globally optimally with high complexity and locally optimally with lower complexity. We then present rounding methods to further reduce computation complexity of the second dynamic programming-based algorithm at the expense of degrading solution quality. Results show that our low-complexity dynamic programming algorithm achieves results comparable to the optimal but high-complexity algorithm, and that gradual tradeoff between complexity and optimization quality can be achieved by our rounding techniques
22 citations
TL;DR: An energy-optimal distributed algorithm is given that constructs an optimal MST with energy complexity O(log n) on average and O( log n log log n) with high probability, an improvement over the previous best known bound on the average energy complexity of Omega(log2 n).
Abstract: Traditionally, the performance of distributed algorithms has been measured in terms of time and message complexity.Message complexity concerns the number of messages transmitted over all the edges during the course of the algorithm. However, in energy-constrained ad hoc wireless networks (e.g., sensor networks), energy is a critical factor in measuring the efficiency of a distributed algorithm. Transmitting a message between two nodes has an associated cost (energy) and moreover this cost can depend on the two nodes (e.g., the distance between them among other things). Thus in addition to the time and message complexity, it is important to consider energy complexity that accounts for the total energy associated with the messages exchanged among the nodes in a distributed algorithm. This paper addresses the minimum spanning tree (MST) problem, a fundamental problem in distributed computing and communication networks. We study energy-efficient distributed algorithms for the Euclidean MST problem assuming random distribution of nodes. We show a non-trivial lower bound of Omega(log n) on the energy complexity of any distributed MST algorithm. We then give an energy-optimal distributed algorithm that constructs an optimal MST with energy complexity O(log n) on average and O(log n log log n) with high probability. This is an improvement over the previous best known bound on the average energy complexity of Omega(log2 n). Our energy-optimal algorithm exploits a novel property of the giant component of sparse random geometric graphs. All of the above results assume that nodes do not know their geometric coordinates. If the nodes know their own coordinates, then we give an algorithm with O(1) energy complexity (which is the best possible) that gives an O(1) approximation to the MST.
22 citations
08 Jul 1991
TL;DR: This work attempts to motivate, justify and survey the average case reduction theory, and shows how the theory can be motivated, justified and surveyed.
Abstract: We attempt to motivate, justify and survey the average case reduction theory.
22 citations
15 Jul 2009
TL;DR: In this paper, it was shown that the communication complexity of the function f(x, y) = T(x \circ y) is O(n/4^d) where (x √ y) was defined so that the resulting tree also has alternating levels of AND and OR gates.
Abstract: We study the 2-party randomized communication complexity of read-once AC0 formulae. For balanced AND-OR trees T with n inputs and depth d, we show that the communication complexity of the function f(x, y) = T(x \circ y) is \Omega(n/4^d) where (x \circ y) is defined so that the resulting tree also has alternating levels of AND and OR gates. For each bit of x \circ y, the operation \circ is either AND or OR depending on the gate in T to which it is an input. Using this, we show that for general AND-OR trees T with n inputs and depth d, the communication complexity of f (x \circ y) is n/2^{\O(d log d)}. These results generalize classical results on the communication complexity of set-disjointness [1], [2] (where T is an OR -gate) and recent results on the communication complexity of the TRIBES functions [3] (where T is a depth-2 read-once formula). Our techniques build on and extend the information complexity methodology [4], [5], [3] for proving lower bounds on randomized communication complexity. Our analysis for trees of depth d proceeds in two steps: (1) reduction to measuring the information complexity of binary depth-d trees, and (2) proving lower bounds on the information complexity of binary trees. In order to execute this program, we carefully construct input distributions under which both these steps can be carried out simultaneously. We believe the tools we develop will prove useful in further studies of information complexity in particular, and communication complexity in general.
22 citations
22 citations