"... In PAGE 16: ... In our experiments, we considered only single layer and two layer routing. Table1 gives the average percentage by which the area of the single layer solutions generated by each of the heuristics exceeded the area of the single layer optimal solution. As is evident, each of the heuristics proposed in this paper gave noticeably better solutions than did Fang.... ..."

"... In PAGE 16: ... The measure of distance to feasibility (the {tube strategy), the nonmonotone updating of penalty parameter d, and the trust region strategy were essentially dormant during the solution process regardless of the iterates apos; proximity to the solution or to feasibility. In fact, the only evidence of our enhancements on the small number of CUTE test problems that we solved occurred when d was decreased slightly while solving the problem MANNE employing modi ed Hessians with a trust region strategy (see the third and fourth rows of Table7 ). It is noteworthy that the iterates that resulted from solving this problem with the penalty parameter arti cially held xed at d = 1 were identical to iterates that resulted for the adjusted d solution.... ..."

"... In PAGE 4: ... Seller incentive-compatibility implies that a seller cannot bene#0Ct from manipulating the price of any item she is selling, either by the use of a shill #28a third party#29 or by placing a bid herself. We present these properties over a space of auction types in Table1 . The incentive-compatibility properties are standard #28see McAfee and McMillan #281987#29, for example#29.... In PAGE 6: ... Traditional considerations of the cognitive costs of auctions include the cost of strategic bidding in a non-incentive compatible auction. Clearly, incentive- compatible auctions require less computation by bidders than auctions which are not incentive-compatible, and thus are preferable #28I C B , Table1 #29. Estimating howmuch other bidders are willing to pay #28in order to bid slightly more than what one thinks the second highest bidder will bid#29 is not easy, although in agent-mediated auctions this cost can be transferred from a human participant to its bidding agent, and is less important than in traditional auctions.... In PAGE 7: ... A bidding agent only needs to know the true value when other buyers have similar reservation prices. We assume that it takes less e#0Bort for a buyer to place bounds on her value for a good than it does to compute her exact value for a good, and therefore prefer auctions that are #5Creservation-price- not-necessary quot; #28 nRP, Table1 #29. Communication costs in on-line auctions are muchlower than in o#0B-line auc- tions #28Beam et al.... In PAGE 7: ... An institutional solution to untrusted auctioneers in on-line Vickrey auctions is to provide trust-certi#0Ced third parties that operate the auctions. The English auction is also susceptible to seller manipulation, but strategic action is not risk-free, and requires the help of a third-party, known as a shill #28I C S , Table1... In PAGE 8: ... The auction should be buyer- incentive-compatible #28I C B #29 to make strategic bidding unnecessary, and reservation- price-not-necessary #28nRP#29 to enable progressive reasoning. We can see from Table1 that the two auction formats with these properties #28ignoring the redun- dant ascending second-price auction#29 are the ascending #0Crst-price and descend- ing second-price auctions. Even with a trusted auctioneer, the Vickrey auction is not suitable because we wish to avoid the high cognitive cost of computing the reservation price for every auction.... ..."

"... In PAGE 12: ...3 and 20 CPU seconds, respectively. In Table2 the number of equilibrium routes, the number of equilibrium routes per O{D pair, and the entropy value for the route ow solution are presented for the DSD, FW, and the most likely route ow solution (the number in the parenthesis is the number of enumerated equilibrium routes). Table 2: Solution data for the Sioux Falls network.... ..."

"... In PAGE 13: ... The computational time for the route enumeration and the solution of the entropy problem is 64 and 970 CPU seconds, respectively. The number of equilibrium routes with signi cant route ow, the number of routes per O{D pair and the entropy value are given in Table5 . Although... ..."

"... In PAGE 25: ...The surveyed protocols base their proposed solutions to the problem of secure ad hoc routing on certain assumptions and operational requirements. Table1 summarizes the results of the comparison regarding this aspect and forms a basis for the discussion in this section. Table 1.... ..."