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We study an abstract setting, where the basic information units (called “superpackets”) do not fit into a single packet, and are therefore spread over multiple packets. We assume that a superpacket is useful only if the number of its delivered packets is above a certain threshold. Our focus of attention is communication link ingresses, where large arrival bursts result in dropped packets. The algorithmic...
We give the first improvement to the space/approximation trade-off of distance oracles since the seminal result of Thorup and Zwick [STOC'01]. For unweighted graphs, our distance oracle has size O(n5/3) = O(n1.66⋯) and, when queried about vertices at distance d, returns a path of length 2d + 1. For weighted graphs with m = n2/α edges, our distance oracle has size O(n2/3√α) and returns a factor 2 approximation...
In this work, we consider the adaptive capacity utilization problem for real-time heterogeneous data intensive MPLS (multiprotocol label switching) networks consisting of multiple source and destination nodes. We account for a file transfer scenario taking into account node capacity, file size, file transfer start time, and the deadline of files when determining the explicit capacity of virtual paths...
The bounded diameter minimum spanning tree problem is an NP-hard combinatorial optimization problem arising for example in network design when quality of service is of concern. We solve a strong integer linear programming formulation based on so-called jump cuts by a novel branch&cut algorithm, using various heuristics including tabu search to solve the separation problem.
It is shown that the problem of deciding and constructing a perfect matching in bipartite graphs G with the polynomial permanents of their n × n adjacency matrices A (perm(A) = nO(1)) are in the deterministic classes NC2 and NC3, respectively. We further design an NC3 algorithm for the problem of constructing all perfect matchings (enumeration problem) in a graph G with a permanent bounded by O(nk)...
In this paper we introduce a model of Hierarchical Memory with Block Transfer (BT for short). It is like a random access machine, except that access to location x takes time f(x), and a block of consecutive locations can be copied from memory to memory, taking one unit of time per element after the initial access time. We first study the model with f(x) = xα for 0 ≪ α ≪ 1. A tight bound of θ(n log...
We describe two methods for obtaining lower bounds on the cost of accessing a sequence of nodes of a symmetrically ordered binary search tree, where rotations can be done on the tree. The bounds apply to offline as well as online algorithms.
We consider the problem of approximating an integer program by first solving its relaxation linear program and "rounding" the resulting solution. For several packing problems, we prove probabilistically that there exists an integer solution close to the optimum of the relaxation solution. We then develop a methodology for converting such a probabilistic existence proof to a deterministic...
We present efficient algorithms for the following geometric problems: (i) Preprocessing of a 2-D polyhedral terrain so as to support fast ray shooting queries from a fixed point. (ii) Determining whether two disjoint interlocking simple polygons can be separated from one another by a sequence of translations. (iii) Determining whether a given convex polygon can be translated and rotated so as to fit...
Sublinear signal propagation delay in VLSI circuits carries a far greater penalty in wire area than is commonly realized. Therefore, the global complexity of VLSI circuits is more layout dependent than previously thought. This effect will be truly pronounced in the emerging wafer scale integration technology. We establish lower bounds on the trade-off between sublinear signalling speed and layout...
We explicitly construct, for every integer n and ε ≫ 0, a family of functions (psuedo-random bit generators) fn,ε:{0,1}nε → {0,1}n with the following property: for a random seed, the pseudorandom output "looks random" to any polynomial size, constant depth, unbounded fan-in circuit. Moreover, the functions fn,ε themselves can be computed by uniform polynomial size, constant depth circuits...
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