### Table 2: Algorithm to Compute Critical Path Length.

"... In PAGE 42: ... The heart of PERT is a network of tasks needed to complete a project, showing the order in which the tasks need to be completed and their dependencies between them. As shown in Table2 , PERT scheduling reduces to a derivate of Dijkstra apos;s single shortest path algorithm within acyclic graphs (Cormen, Leiserson, amp;Rivest, 1990). In the algorithm, e(O i ) is the tentative earliest end time of operator O i , i 2f1;;:::;;kg, while the earliest starting times t i for all operators in the optimal plan are given by t i = e(O i );d(O i ).... In PAGE 93: ... Additionally, if we have to cope with reactive scheduling then feasible solutions and user interaction will become more important. Table2 . Evaluation of the results solution late orders lateness transport costs 1 2 (1 product) 12 24 2 3 (2 products) 8 22 3 2 (2 products) 9 23 4 4 (3 products) 14 21 For a solution approach it is necessary to describe what information is needed to model the problem and how it is used.... ..."

### Table 2. The algorithm to compute regular curves from Sw(V;A). A source in Aj is a vertex with no in-arcs. In line 6, ver(Aj) denotes the set of vertices of the graph Aj. The procedure maximalPath(sj;Aj) returns a maximal path in Aj with starting point sj (see Section 6.1).

1996

"... In PAGE 16: ... Since Uw( j) is a neighborhood of ( j), all the vertices of j belong to Uw( j), except for the two end-points (which belong to the boundary of Uw( j)). Thus, if j has at least three vertices, then no arc of j belongs to Aj+1 because every arc of j has at least one vertex in Uw( j) (see lines 6 and 7 of Table2 ). That is, we have arcs( j) \ Aj+1 = ; (21) where arcs( j) denotes the arcs belonging the the path j.... In PAGE 16: ... That is, we have arcs( j) \ Aj+1 = ; (21) where arcs( j) denotes the arcs belonging the the path j. If j has just two vertices, then one needs to modify slightly the algorithm shown in Table2 so that (21) is still true. We omit these details for the sake of simplicity.... In PAGE 17: ...1. Computing the optimal path The algorithm in Table2 contains the proce- dure maximalPath(sj; Aj) which returns a path j 2 Mj(sj), where Mj(sj) denotes the set of maximal paths in Aj with rst element sj. No- tice that Theorem 5 holds for any choice of a path in Mj(sj).... In PAGE 19: ...elephone image. The nal result is shown in (d). To check whether the cycle is regular it is su - cient to pick one of its vertices and verify whether it is enclosed by either + w( ) or ? w ( ). If the cy- cle is regular then the path maximalPath(sj; Aj) in (25) is set equal to this cycle and lines 7,8 of the procedure in Table2 are applied to it. If the cycle is a looplet then all its nodes are coalesced into a \super-node quot; and the procedure optimize0 continues from this new super-node.... In PAGE 27: ... Notice that Bj Aj. The following must be proven: N [ j=1 Bj = Sw(V; A) = A1 (36) Bj \ Bk = ;; k gt; j (37) From the recursive de nition of Aj (lines 6 and 7 of Table2 ) we have Aj+1 = Aj ? Qj = Aj n f(p1; p2) 2 Aj : p1 2 Uj _ p2 2 Ujg and therefore Aj+1 = Aj n Bj (38) From this it follows that Bj \ Aj+1 = ;. Thus, if k gt; j we have Bj \ Bk = ; because Bk Ak Aj+1.... ..."

### Table 1.7 Ontario Health Insurance Plan (OHIP) fee codes for computed tomography (CT)

2007

### Table 1. Technological improvements in the first 20 years of computed tomography [7].

"... In PAGE 3: ... 4 X-ray CT imaging Computed Tomography (CT) was the first non-invasive radio- logical method allowing the generation of tomographic images of all parts of the human body without superposition of neigh- boring structures. CT imaging has gone through a radial im- provement since its introduction in 1972 ( Table1 ). Today, a CT scanner is a crucial part of any real radiological department.... ..."

### Table 1. Technological improvements in the first 20 years of computed tomography [7].

"... In PAGE 3: ... 4 X-ray CT imaging Computed Tomography (CT) was the first non-invasive radio- logical method allowing the generation of tomographic images of all parts of the human body without superposition of neigh- boring structures. CT imaging has gone through a radial im- provement since its introduction in 1972 ( Table1 ). Today, a CT scanner is a crucial part of any real radiological department.... ..."

### Table 3: The planning algorithm.

2000

"... In PAGE 19: ... 4.3 The Planning Algorithm The progression algorithm admits the planning algorithm shown in Table3 . This algorithm is used in the TLPLAN system described in Section 6.... In PAGE 20: ...4). The planning algorithm specified in Table3 searches for plans that transforms the initial world to a world satisfying the goal. It searches for this plan in the space of action sequences emanating from the initial world and eliminating from that search space some set of plan prefixes.... In PAGE 27: ... If the atomic formula is a computed predicate, then again we take the value returned by the computation to define the predicate. 6 The TLPLAN System We have constructed a planning system called the TLPLAN system that utilizes the planning algo- rithm shown in Table3 . In this section we describe the system and supply some final details about the design of the system.... ..."

Cited by 200

### Table 3: The planning algorithm.

2000

"... In PAGE 19: ... 4.3 The Planning Algorithm The progression algorithm admits the planning algorithm shown in Table3 . This algorithm is used in the TLPLAN system described in Section 6.... In PAGE 20: ...4). The planning algorithm specified in Table3 searches for plans that transforms the initial world to a world satisfying the goal. It searches for this plan in the space of action sequences emanating from the initial world and eliminating from that search space some set of plan prefixes.... In PAGE 27: ... If the atomic formula is a computed predicate, then again we take the value returned by the computation to define the predicate. 6 The TLPLAN System We have constructed a planning system called the TLPLAN system that utilizes the planning algo- rithm shown in Table3 . In this section we describe the system and supply some final details about the design of the system.... ..."

Cited by 200

### Table 1. First occurrences of prime gaps in 7:2 1013 lt;p lt;1015

"... In PAGE 3: ... 3. Computational results Table1 lists the rst occurrences of prime gaps found in the present study, now complete to 1015. The new maximal gaps are marked with an asterisk ( ).... In PAGE 3: ... The smallest gap whose rst occurrence is still unaccounted for is the gap of 796. First occurrences of all gaps greater than 796, not listed in Table1 , also remain to be discovered. Discovery of the new maximal gap of 906 brings us closer to the goal alluded to by Weintraub [16], that of nding the rst occurrence of a gap of 1000 or greater.... ..."

### Table 1: Overview of path planning techniques

2000

"... In PAGE 2: ... Path planning techniques generally proceed in two phases: in the rst phase a representation of the connectivity of the free space is computed; this representation is then used in the second phase to determine a solution to the given path planning problem. Table1 presents an overview of how var- ious planning methods address these two phases. It is noteworthy that all approaches reduce the second phase to a computationally simple problem: either gradient descent or graph search.... ..."

Cited by 2

### Table 1: Overview of path planning techniques

2000

"... In PAGE 2: ... Path planning techniques generally proceed in two phases: in the first phase a representation of the connectivity of the free space is computed; this representation is then used in the second phase to determine a solution to the given path planning problem. Table1 presents an overview of how var- ious planning methods address these two phases. It is noteworthy that all approaches reduce the second phase to a computationally simple problem: either gradient descent or graph search.... ..."

Cited by 2