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Minimumenergy multicast in mobile ad hoc networks using network coding
 IEEE Trans. Commun
, 2005
"... Abstract — The minimum energy required to transmit a bit of information through a network characterizes the most economical way to communicate in a network. In this paper, we show that under a layered model of wireless networks, the minimum energyperbit for multicasting in a mobile ad hoc network c ..."
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Cited by 89 (2 self)
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Abstract — The minimum energy required to transmit a bit of information through a network characterizes the most economical way to communicate in a network. In this paper, we show that under a layered model of wireless networks, the minimum energyperbit for multicasting in a mobile ad hoc network can be found by a linear program; the minimum energyperbit can be attained by performing network coding. Compared with conventional routing solutions, network coding not only promises a potentially lower energyperbit, but also enables the optimal solution to be found in polynomial time, in sharp contrast with the NPhardness of constructing the minimumenergy multicast tree as the optimal routing solution. We further show that the minimum energy multicast formulation is equivalent to a cost minimization with linear edgebased pricing, where the edge prices are the energyperbits of the corresponding physical broadcast links. This paper also investigates minimum energy multicasting with routing. Due to the linearity of the pricing scheme, the minimum energyperbit for routing is achievable by using a single distribution tree. A characterization of the admissible rate region for routing with a single tree is presented. The minimum energyperbit for multicasting with routing is found by an integer linear program. We show that the relaxation of this integer linear program, studied earlier in the Steiner tree literature, can now be interpreted as the optimization for minimum energy multicasting with network coding. In short, this paper presents a unifying study of minimum energy multicasting with network coding and routing. Index Terms — Network coding, routing, multicast, Steiner tree, wireless ad hoc networks, energy efficiency, mobility.
A General Stochastic Approach to Solving Problems with Hard and Soft Constraints
 The Satisfiability Problem: Theory and Applications
, 1996
"... . Many AI problems can be conveniently encoded as discrete constraint satisfaction problems. It is often the case that not all solutions to a CSP are equally desirable  in general, one is interested in a set of "preferred" solutions (for example, solutions that minimize some cost function) . Pref ..."
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Cited by 46 (1 self)
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. Many AI problems can be conveniently encoded as discrete constraint satisfaction problems. It is often the case that not all solutions to a CSP are equally desirable  in general, one is interested in a set of "preferred" solutions (for example, solutions that minimize some cost function) . Preferences can be encoded by incorporating "soft" constraints in the problem instance. We show how both hard and soft constraints can be handled by encoding problems as instances of weighted MAXSAT (finding a model that maximizes the sum of the weights of the satisfied clauses that make up a problem instance). We generalize a localsearch algorithm for satisfiability to handle weighted MAXSAT. To demonstrate the effectiveness of our approach, we present experimental results on encodings of a set of wellstudied network Steinertree problems. This approach turns out to be competitive with some of the best current specialized algorithms developed in operations research. 1. Introduction Traditi...
Solving Problems with Hard and Soft Constraints Using a Stochastic Algorithm for MAXSAT
, 1995
"... Stochastic local search is an effective technique for solving certain classes of large, hard propositional satisfiability problems, including propositional encodings of problems such as circuit synthesis and graph coloring (Selman, Levesque, and Mitchell 1992; Selman, Kautz, and Cohen 1994). Many pr ..."
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Cited by 42 (3 self)
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Stochastic local search is an effective technique for solving certain classes of large, hard propositional satisfiability problems, including propositional encodings of problems such as circuit synthesis and graph coloring (Selman, Levesque, and Mitchell 1992; Selman, Kautz, and Cohen 1994). Many problems of interest to AI and operations research cannot be conveniently encoded as simple satisfiability, because they involve both hard and soft constraints  that is, any solution may have to violate some of the less important constraints. We show how both kinds of constraints can be handled by encoding problems as instances of weighted MAXSAT (finding a model that maximizes the sum of the weights of the satisfied clauses that make up a problem instance). We generalize our localsearch algorithm for satisfiability (GSAT) to handle weighted MAXSAT, and present experimental results on encodings of the Steiner tree problem, which is a wellstudied hard combinatorial search problem. On many...