How Good are Genetic Algorithms at Finding Large Cliques: An Experimental Study

This paper investigates the power of genetic algorithms at solving the MAX-CLIQUE problem. We measure the performance of a standard genetic algorithm on an elementary set of problem instances consisting of embedded cliques in random graphs. We indicate the need for improvement, and introduce a new genetic algorithm, the multi-phase annealed GA, which exhibits superior performance on the same problem set. As we scale up the problem size and test on \hard" benchmark instances, we notice a degraded performance in the algorithm caused by premature convergence to local minima. To alleviate this problem, a sequence of modi cations are implemented ranging from changes in input representation to systematic local search. The most recent version, called union GA, incorporates the features of union cross-over, greedy replacement, and diversity enhancement. It shows a marked speed-up in the number of iterations required to find a given solution, as well as some improvement in the clique size found. We discuss issues related to the SIMD implementation of the genetic algorithms on a Thinking Machines CM-5, which was necessitated by the intrinsically high time complexity (O(n3)) of the serial algorithm for computing one iteration. Our preliminary conclusions are: (1) a genetic algorithm needs to be heavily customized to work "well" for the clique problem; (2) a GA is computationally very expensive, and its use is only recommended if it is known to find larger cliques than other algorithms; (3) although our customization e ort is bringing forth continued improvements, there is no clear evidence, at this time, that a GA will have better success in circumventing local minima.

Open Issues on TCP for Mobile Computing

We discuss the design principles of TCP within the context of heterogeneous wired/wireless networks and mobile networking. We identify three shortcomings in TCP's behavior: (i) the protocol's error detection mechanism, which does not distinguish different types of errors and thus does not suffice for heterogeneous wired/wireless environments, (ii) the error recovery, which is not responsive to the distinctive characteristics of wireless networks such as transient or burst errors due to handoffs and fading channels, and (iii) the protocol strategy, which does not control the tradeoff between performance measures such as goodput and energy consumption, and often entails a wasteful effort of retransmission and energy expenditure. We discuss a solution-framework based on selected research proposals and the associated evaluation criteria for the suggested modifications. We highlight an important angle that did not attract the required attention so far: the need for new performance metrics, appropriate for evaluating the impact of protocol strategies on battery-powered devices.