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Spanning subgraph is necessary for the communication in networks. For example, the malfunctioning of one or more nodes in a network in general affects both the global and the local properties of the remaining nodes, because it makes some edges unusable and destroys the connectivity of the system. In this study, we focus on the characters of a network to be fractional-r-factors, fractional (r, k)-extendable...
We present a near-linear time algorithm that approximates the edit distance between two strings within a polylogarithmic factor. For strings of length n and every fixed ε >; 0, the algorithm computes a (log n)O(1/ε) approximation in n1+ε time. This is an exponential improvement over the previously known approximation factor, 2Õ(√log n), with a comparable running time [Ostrovsky and Rabani, J....
We investigate the possibility of finding satisfying assignments to Boolean formulae and testing validity of quantified Boolean formulae (QBF) asymptotically faster than a brute force search. Our first main result is a simple deterministic algorithm running in time 2n-Ω(n) for satisfiability of formulae of linear size in n, where n is the number of variables in the formula. This algorithm extends...
Let G be a directed edge-weighted graph and let P be a shortest path from s to t in G. The replacement paths problem asks to compute, for every edge e on P, the shortest s-to-t path that avoids e. Apart from approximation algorithms and algorithms for special graph classes, the naive solution to this problem - removing each edge e on P one at a time and computing the shortest s-to-t path each time...
We consider the following general scheduling problem: The input consists of n jobs, each with an arbitrary release time, size, and a monotone function specifying the cost incurred when the job is completed at a particular time. The objective is to find a preemptive schedule of minimum aggregate cost. This problem formulation is general enough to include many natural scheduling objectives, such as...
It is widely suspected that Erdös-Renyi random graphs are a source of hard instances for clique problems. Giving further evidence for this belief, we prove the first average-case hardness result for the k-clique problem on monotone circuits. Specifically, we show that no monotone circuit of size O(nk/4) solves the k-clique problem with high probability on G(n,p) for two sufficiently far-apart threshold...
We give a subexponential time approximation algorithm for the Unique Games problem. The algorithms run in time that is exponential in an arbitrarily small polynomial of the input size, nε. The approximation guarantee depends on ε, but not on the alphabet size or the number of variables. We also obtain a subexponential algorithms with improved approximations for SMALL-SET EXPANSION and MULTICUT. For...
In the paper, a modified Log-MAP algorithm based on a novel approximation of the max* operator derived from the Jensen inequality is proposed. In this approach, the max* operation is performed on n≥2 arguments, thus the recursive calculations are avoided and significant reduction in the number of operations performed per decoding step, as compared with the conventional Log-MAP, is achieved. Simulation...
While there has been substantial research on the integration of grid-based and topological maps, no previous approach, to our knowledge, has considered constructing hybrid maps applying the maximal empty rectangle problem found in computational geometery. We propose a hybrid map, R-Map, which is built by extracting a topological information out of a grid map by a simple rule; Find the largest free...
In this paper, the combined normalized and offset min-sum algorithm is proposed for efficient decoding of low-density parity-check (LDPC) codes in optical and magnetic storage systems. The proposed algorithm can be considered as a general case of the normalized and offset algorithms, and offers better BER performance compared to them. The performance improvement is presented for a partial response...
Broadcasting is an information dissemination problem in a connected network, in which one node, called the originator, disseminates a message to all other nodes by placing a series of calls along the communication lines of the network. Once informed, the nodes aid the originator in distributing the message. Finding the minimum broadcast time of a vertex in an arbitrary graph is NP-complete. The problem...
Recently, there have been papers indicating that the maximal ratio combiner device can result in energy savings in wireless ad hoc networks by using hitch-hiking. We study the min-energy broadcast with hitch-hiking problem, an idealized version of broadcast using hitch-hiking, a problem studied experimentally in the INFOCOM 2004 paper of Agarwal et al. min-energy broadcast with hitch-hiking captures...
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