"... In PAGE 15: ... Localization queries have a very small accumulated running time, showing that pre-computation is crucial. In Table2 we depict the running time of the sweep-line algorithm as well as the effect of heuristic search, where tg is the time of the sweep-line algorithm, tc is the preparation time of the search algorithm (initializing the data structures) ts is the pure searching time for a single shortest path query, and #exp is the corresponding number of expansions done in computing the shortest path. As in the case of point localization the sweep-line intersection algorithm is more... In PAGE 16: ... Heuristic search can suc- cessfully be combined with geometric pruning. The smaller impact of heuristic search compared to Table2 can be attributed to the averaging effect of random queries, posing... ..."

"... In PAGE 5: ... Using the settings (5 j j 85 ; = f0:2; 1:0g), the backtracking (A) and heuristic (B) searches were run on all 300 polygons. The total number of failures (A-fail, B-fail) and total number of states (A-states, B-states) examined to find solutions are given in Table1 . The heuristic search was stopped after 500 iterations.... ..."

"... In PAGE 14: ... 4 Also the running times are very good. 5 Consistently with #28Manzini, 1995, Table1 #29, Fig. 4 shows a steady decrease of both the number of nodes generated and the required running time for increasing perimeter depth until it reaches 16.... In PAGE 30: ... Discussion After this presentation of our new approach to bidirectional heuristic search and its exper- imental results, let us put it into perspective. Table1 provides an overview of the existing approaches according to the wayofevaluating and the way of organizing the change#28s#29 of search direction. The algorithms that instantiate our new generic approach fall into the category of non-traditional bidirectional heuristic search algorithms #28that change the search direction only once#29 and that perform front-to-end evaluations.... In PAGE 30: ... However, it has less overhead and is therefore more e#0Ecient per node searched in terms of running time. From the viewpointof Table1 , our approach somehow #5Ccompletes quot; the picture of bidi- rectional heuristic search. #28Note, however, that the non-traditional approachwas found independently of the work on perimeter search.... In PAGE 31: ..., 1989; Sen amp; Bagchi, 1989; Russell, 1992; Ghosh et al., 1994; Reinefeld amp; Marsland, 1994#29 than the non-traditional approaches to bidirectional searchasshown in Table1 . In particular, our generic approach allows very #0Dexible and e#0Bective use of available memory.... ..."

"... In PAGE 5: ... We have three terabytes of disk storage available, consisting of four 500 gigabyte Firewire external drives, and a 400 and two 300 gigabyte internal Serial ATA drives. Table2 shows our results. The first column shows the num- ber of discs, the second column the optimal solution length to transfer all discs from one peg to another, the third column the radius of the problem space from the standard initial state, the fourth column the width of the problem space, which is the maximum number of unique states at any depth from the standard initial state, and the last column the running time in days:hours:minutes:seconds, running six parallel threads.... ..."

"... In PAGE 33: ...Table 10: Performance of Level and Sum heuristics in searching longer planning graphs Table 9 shows the performance of Graphplan with the Max heuristic, when the search is conducted starting from the level where minimum length solution occurs, as well as 3, 5 and 10 levels above this level. Table10 shows the same experiments with with the Level and Sum heuristics. The results in these tables show that Graphplan with a level-based variable and value ordering heuristic is surprisingly robust with respect to searching on longer planning graphs.... ..."