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418
Polynomial time algorithms for multicast network code construction
 IEEE Trans. on Info. Thy
"... Abstract—The famous maxflow mincut theorem states that a source node can send information through a network ( ) to a sink node at a rate determined by the mincut separating and. Recently, it has been shown that this rate can also be achieved for multicasting to several sinks provided that the int ..."
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Cited by 183 (15 self)
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Abstract—The famous maxflow mincut theorem states that a source node can send information through a network ( ) to a sink node at a rate determined by the mincut separating and. Recently, it has been shown that this rate can also be achieved for multicasting to several sinks provided that the intermediate nodes are allowed to reencode the information they receive. We demonstrate examples of networks where the achievable rates obtained by coding at intermediate nodes are arbitrarily larger than if coding is not allowed. We give deterministic polynomial time algorithms and even faster randomized algorithms for designing linear codes for directed acyclic graphs with edges of unit capacity. We extend these algorithms to integer capacities and to codes that are tolerant to edge failures. Index Terms—Communication networks, efficient algorithms, linear coding, multicasting rate maximization. I.
Admissible Heuristics for Optimal Planning
 In Proceedings of AIPS00
, 2000
"... hsp and hspr are two recent planners that search the statespace using an heuristic function extracted from Strips encodings. hsp does a forward search from the initial state recomputing the heuristic in every state, while hspr does a regression search from the goal computing a suitable representati ..."
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Cited by 169 (21 self)
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hsp and hspr are two recent planners that search the statespace using an heuristic function extracted from Strips encodings. hsp does a forward search from the initial state recomputing the heuristic in every state, while hspr does a regression search from the goal computing a suitable representation of the heuristic only once. Both planners have shown good performance, often producing solutions that are competitive in time and number of actions with the solutions found by Graphplan and sat planners. hsp and hspr, however, are not optimal planners. This is because the heuristic function is not admissible and the search algorithms are not optimal. In this paper we address this problem. We formulate a new admissible heuristic for planning, use it to guide an ida search, and empirically evaluate the resulting optimal planner over a number of domains. The main contribution is the idea underlying the heuristic that yields not one but a whole family of polynomial and admissible heuristics that trade accuracy for e ciency. The formulation is general and sheds some light on the heuristics used in hsp and Graphplan, and their relation. It exploits the factored (Strips) representation of planning problems, mapping shortestpath problems in statespace into suitably dened shortestpath problems in atomspace. The formulation applies with little variation to sequential and parallel planning, and problems with di erent action costs.
An Efficient Implementation Of A Scaling MinimumCost Flow Algorithm
 Journal of Algorithms
, 1992
"... . The scaling pushrelabel method is an important theoretical development in the area of minimumcost flow algorithms. We study practical implementations of this method. We are especially interested in heuristics which improve reallife performance of the method. Our implementation works very well o ..."
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Cited by 99 (7 self)
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. The scaling pushrelabel method is an important theoretical development in the area of minimumcost flow algorithms. We study practical implementations of this method. We are especially interested in heuristics which improve reallife performance of the method. Our implementation works very well over a wide range of problem classes. In our experiments, it was always competitive with the established codes, and usually outperformed these codes by a wide margin. Some heuristics we develop may apply to other network algorithms. Our experimental work on the minimumcost flow problem motivated theoretical work on related problems. Supported in part by ONR Young Investigator Award N0001491J1855, NSF Presidential Young Investigator Grant CCR8858097 with matching funds from AT&T and DEC, Stanford University Office of Technology Licensing, and a grant form the Powell Foundation. 1 1. Introduction. Significant theoretical progress has been made recently in the area of minimumcost flow ...
Polynomial Time Algorithms for Network Information Flow
 in 15th ACM Symposium on Parallel Algorithms and Architectures
, 2003
"... The famous maxflow mincut theorem states that a source node s can send information through a network (V; E) to a sink node t at a data rate determined by the mincut separating s and t. Recently it has been shown that this rate can also be achieved for multicasting to several sinks provided that t ..."
Abstract

Cited by 96 (1 self)
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The famous maxflow mincut theorem states that a source node s can send information through a network (V; E) to a sink node t at a data rate determined by the mincut separating s and t. Recently it has been shown that this rate can also be achieved for multicasting to several sinks provided that the intermediate nodes are allowed to reencode the information they receive. In contrast, we present graphs where without coding the rate must be a factor jV j) smaller. However, so far no fast algorithms for constructing appropriate coding schemes were known. Our main result are polynomial time algorithms for constructing coding schemes for multicasting at the maximal data rate.
Decoding ErrorCorrecting Codes via Linear Programming
, 2003
"... Abstract. Errorcorrecting codes are fundamental tools used to transmit digital information over unreliable channels. Their study goes back to the work of Hamming [Ham50] and Shannon [Sha48], who used them as the basis for the field of information theory. The problem of decoding the original informa ..."
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Cited by 79 (6 self)
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Abstract. Errorcorrecting codes are fundamental tools used to transmit digital information over unreliable channels. Their study goes back to the work of Hamming [Ham50] and Shannon [Sha48], who used them as the basis for the field of information theory. The problem of decoding the original information up to the full errorcorrecting potential of the system is often very complex, especially for modern codes that approach the theoretical limits of the communication channel. In this thesis we investigate the application of linear programming (LP) relaxation to the problem of decoding an errorcorrecting code. Linear programming relaxation is a standard technique in approximation algorithms and operations research, and is central to the study of efficient algorithms to find good (albeit suboptimal) solutions to very difficult optimization problems. Our new “LP decoders ” have tight combinatorial characterizations of decoding success that can be used to analyze errorcorrecting performance. Furthermore, LP decoders have the desirable (and rare) property that whenever they output a result, it is guaranteed to be the optimal result: the most likely (ML) information sent over the
Auction algorithms for network flow problems: A tutorial introduction
 Comput. Optim. Appl
, 1992
"... by ..."
Energy Efficient Routing in Ad Hoc Disaster Recovery Networks
, 2003
"... The terrorist attacks on September 11, 2001 have drawn attention to the use of wireless technology in order to locate survivors of structural collapse. We propose to construct an ad hoc network of wireless smart badges in order to acquire information from trapped survivors. We investigate the energy ..."
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Cited by 60 (2 self)
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The terrorist attacks on September 11, 2001 have drawn attention to the use of wireless technology in order to locate survivors of structural collapse. We propose to construct an ad hoc network of wireless smart badges in order to acquire information from trapped survivors. We investigate the energy efficient routing problem that arises in such a network and show that since smart badges have very Hmited power sources and very low data rates, which may be inadequate in an emergency situation, the solution of the routing problem requires new protocols. The problem is formulated as an anycast routing problem in which the objective is to maximize the time until the first battery drainsout. We present iterative algorithms for obtaining the optimal solution of the problem. Then, we derive an upper bound on the network lifetime for specific topologies. Finally, a polynomial algorithm for obtaining the optimal solution in such topologies is described.
A case study of multiservice, multipriority traffic engineering design for data networks
 in Proc. IEEE GLOBECOM
, 1999
"... ..."
Dijkstra's Algorithm OnLine: An Empirical Case Study from Public Railroad Transport
 JOURNAL OF EXPERIMENTAL ALGORITHMICS
, 2000
"... ..."
Efficiently Solving Dynamic Markov Random Fields using Graph Cuts
 in: IEEE International Conference on Computer Vision (ICCV
, 2005
"... In this paper we present a fast new fully dynamic algorithm for the stmincut/maxflow problem. We show how this algorithm can be used to efficiently compute MAP estimates for dynamically changing MRF models of labelling problems in computer vision, such as image segmentation. Specifically, given th ..."
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Cited by 53 (9 self)
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In this paper we present a fast new fully dynamic algorithm for the stmincut/maxflow problem. We show how this algorithm can be used to efficiently compute MAP estimates for dynamically changing MRF models of labelling problems in computer vision, such as image segmentation. Specifically, given the solution of the maxflow problem on a graph, we show how to efficiently compute the maximum flow in a modified version of the graph. Our experiments showed that the time taken by our algorithm is roughly proportional to the number of edges whose weights were different in the two graphs. We test the performance of our algorithm on one particular problem: the objectbackground segmentation problem for video and compare it with the best known stmincut algorithm. The results show that the dynamic graph cut algorithm is much faster than its static counterpart and enables real time image segmentation. It should be noted that our method is generic and can be used to yield similar improvements in many other cases that involve dynamic change in the graph. 1.