### Table 1. Graph-based modeling approaches.

2007

"... In PAGE 4: ... A transition links any two nodes (task or coordinator) and is represented by a directed arc. Table1 provides a list of representative graph-based modeling approaches. Table 1.... ..."

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### Table 2. Performance of graph-based propagation approach.

2007

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### Table 1 Graph-Based Process Configuration Measures

2002

"... In PAGE 17: ...A sample of graph-based process configuration measures and values is presented in Table1 . The measurements listed under the Process A label are obtained from the example representation presented in Figure 4 above.... In PAGE 22: ... This latter inference represents the kind obtainable only through a ratio scale. A BCD A BC Process A Process C Figure 7 Processes as Standard Sequences To generalize, we can apply the extensive-measurement procedure to the other graph-based measures defined in Table1 as well. For instance, returning to the two directed graphs presented in Figure 7, say we measure a graph-based representation for Process A and obtain a measured value of four for process size.... In PAGE 23: ... As above, we note this is exactly the kind of analysis used to determine the measure mass, used extensively in the physical sciences, which supports a ratio scale. And again, this extensive-measurement approach can be applied to any of the graph-based measures defined in Table1 , in addition to other measures based on like graph-theoretic concepts (e.g.... ..."

### Table 1. Comparison over GraphBase directed graphs.

2005

"... In PAGE 4: ... The first set comes from [8]. The graphs are characterized by their probability (eta = 0:01 is noted r001 in Table1 ) that an edge is present between two distinct node n and n0. Those graphs were used to evaluate vflib algorithm performance [7].... In PAGE 4: ... Experiments show that CSP approach for subgraph matching solves more problem within a time limit against C++ specialized checking-based methods [7]. Table1 and 2 show the percentage of instances solved within a time limit of 5 minutes, for directed and undirected instances. Single specialized propagator MCPA for forbidden edges is more efficient than the version with two propagators.... ..."

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### Table 2: Number of pivots, and accuracy of the CPU time estimators. running times. Since margins only need to be computed for a constant initiation interval, and only involve the precedence constraints, reverting to a graph-based approach instead of using a simplex tableau is likely to yield lower scheduling times. Another direction for experimentation is the removal of the redundancies from the central problems, a task easy to achieve in theory by taking advantage of the simplex tableau representation.

### Table 1: Syntactic domains for the source language We do not bother how variables are represented, we simply assume that there are enough of them. 4Categorical combinatorylogic can be viewed as \classical quot; combinatorylogic augmentedwith products. Categorical combinators have been proposed as an alternative to SK combinators by Lins [20] revealing once again the close interconnection between graph-based and environment-based approaches.

1993

"... In PAGE 3: ... Readers familiar with the topic may safely skip this section. The syntactic domains of the language are shown in Table1 . The domain var contains variables.... In PAGE 16: ... . `n : R[[en]] 0 3 7 5 where 0 = h: : :h ; p1 7! `1i : : :; pn 7! `ni Table1 0: The C scheme revisited for multiple recursive de nitions 5 r-Closed Expressions The compilation schemes which we have introduced in the last section are conceptionally very simple but they are of course too simple-minded to be used in a real implementation. In the following we will introduce several techniques which aim at improving the quality of the generated code (classically called code optimizations).... In PAGE 18: ... r-free : exp ! env (IP var) ! IP var r-free[[x]] h ; pi = fxg if x 2 vars[[p]] = r-free[[x]] otherwise r-free[[x]] h ; p 7! V i = V if x 2 vars[[p]] = r-free[[x]] otherwise r-free[[s(n) e1 en]] = r-free[[e1]] [ [ r-free[[en]] r-free[[()]] = ; r-free[[(e1; e2)]] = r-free[[e1]] [ r-free[[e2]] r-free[[c e]] = r-free[[e]] r-free[[e1 e2]] = r-free[[e1]] [ r-free[[e2]] r-free[[ p ! e]] = r-free[[e]] h ; pi n vars[[p]] r-free[[if e1 then e2 else e3]] = r-free[[e1]] [ r-free[[e2]] [ r-free[[e3]] r-free[[case e of c1 p1 ! e1 j j cn pn ! en]] = r-free[[e]] [ r-free[[e1]] h ; p1i n vars[[p1]] [ [ r-free[[en]] h ; pni n vars[[pn]] r-free[[let p1 = e1 in e]] = (r-free[[e]] h ; p1i n vars[[p1]]) [ r-free[[e1]] r-free[[letrec p1 = e1 ; : : : ; pn = en in e]] = r-free[[e]] 0 where 0 = h: : :h ; p1 7! r-free[[e1]] 0i : : :; pn 7! r-free[[en]] 0i r-closed[[e]] de nes the property of r-closedness relative to the environment . r-closed : exp ! env (IP var) ! bool r-closed[[e]] = r-free[[e]] = ; Table1 1: The computation of r-free variables... In PAGE 19: ... The above example is transformed to the nested expression: e = a b ! letrec g = : : :h : : : ; h = : : :b : : :g : : : in letrec f = : : :a : : :g : : : in : : : For expressions of this kind the last equation of r-free can be simpli ed as indicated in Table 12. The r-free[[letrec p1 = e1 ; : : : ; pn = en in e]] = r-free[[e]] 1 where 0 = h: : :h ; p1 = ;i : : :; pn = ;i V = r-free[[e1]] 0 [ [ r-free[[en]] 0 1 = h: : :h ; p1 = V i : : :; pn = V i Table1 2: The de nition of r-free revisited for truly recursive de nitions modi ed de nition re ects the fact that the de ning expressions are truly recursive.... In PAGE 20: ... Table 14 shows the modi ed compilation schemes. Again we will consider each of them register stack code register stack code stack operations v S Move; C () v : S C v1 v2 : S Pop; C v2 S C register operations v1 v2 : S Snoc; C (v1; v2) S C v S Comb ` ; C [`] S C control instructions [`] v : S App; C v C : S C` true S Gotoifalse ` ; C true S C false S Gotoifalse ` ; C false S C` (ci : v) S Switchi [c1 : `1; : : :; cn : `n] ; C v S C`i Table1 3: Some more instructions in turn. E [[x]] hi = fail E [[x]] h ; pi = E [[x]] E [[x]] h ; p 7! `i = (Call ` ; P[[x]] p) ? E [[x]] E[[x]] h ; pi n = Rest n ; P[[x]] p C[[x ]] = E [[x]] C[[e 1 e2]] = C[[e2]] ; Move; C[[e1]] ; App C[[e1 e 2]] = Move; C[[e2]] ; Swap; C[[e1]] ; App C[[( p ! e) ]] = Comb ` ` : R[[e]] h ; pi C[[if e1 then e 2 else e 3]] = C[[e1]] ; Gotoifalse `1 ; C[[e2]] ; Goto `2 ; `1 : C[[e3]] ; `2 : Skip C[[case e of (c1 p1 ! e1) j j (cn pn ! en) ]] = C[[e]] ; Switchi [c1 : `1; : : :; cn : `n] ; `1 : C[[e1]] h ; p1i ; Goto ` .... In PAGE 20: ... . `n : C[[en]] h ; pni ; ` : Skip C[[let p1 = e1 in e]] = C[[e1]] ; C[[e]] h ; p1i if p1 ! e is r-closed C[[let p1 = e 1 in e]] = Move; C[[e1]] ; Cons; C[[e]] h ; p1i T [[e1; e 2]] = C[[e1]] ; Move; C[[e2]] T [[e 1; e2]] = C[[e2]] ; Move; C[[e1]] ; Swap Table1 4: The E , E, C, and T compilation schemes for r-closed expressions... In PAGE 29: ... . `n : R[[en]] h ; pni ; R[[e]] = C[[e]] ; Return Table1 5: The R compilation scheme for last call optimization The mutual recursive de nitions of even and odd serve as an example for the e ects of last call optimization. letrec even = n ! if = n 0 then true else odd (dec n) ; odd = n ! if = n 0 then false else even (dec n) in even 56 Quote 56 Prim = `3 : Push Return Call `3 Gotofalse `2 Move `4 : Prim dec Stop Quote true Quote 0 Goto `1 `1 : Push Return Prim = Move `2 : Prim dec Gotofalse `4 Quote 0 Goto `3 Quote false 6.... In PAGE 30: ...code improved code o set access instructions Skip ?1 Rest 0 ?1 Rest 1 Fst ?1 Acc 0 Snd ?1 Fst ; Fst Rest 2 0 Fst ; Snd Acc 1 1 Rest n ; Fst Rest (n + 1) if n 2 0 Rest n ; Snd Acc n if n 2 1 stack operations Push ; Swap Push 0 Move; Pop ?1 register operations Swap ; Cons Snoc ?1 Swap ; Snoc Cons ?1 Swap ; Prim s(2) Prim sc (2) ?1 control instructions Cur ` ; App Snoc ; Call ` ?1 Comb ` ; App Pop ; Call ` ?1 Call ` ` : I ; Return I ` : I ; Return ?1 Call ` ; Return Goto ` 1 Table1 6: Optimization rules In the remainder we name some of the advantages and disadvantages of peephole optimizations in contrast to source code transformations like partial evaluation. It is obvious that the compilation of a -expression to a sequence of CAM instructions is a structure loosing mapping.... ..."

### Table 9 Example Process Measures Measure Graph-Based Definition

"... In PAGE 43: ... to support comparative process analysis). A set of example process measures is presented in Table9 , along with their corresponding graph- based definitions. Table 9 Example Process Measures Measure Graph-Based Definition... ..."

### Table 1: Computational Effort for Landmark Graph-Based Registration

2003

"... In PAGE 6: ... 3 Summary of Computational Effort Each of the processing steps requires worst-case effort that has a polynomial bound. The effort described in Table1 assumes: NxM range images and F landmarks. D is the mean degree of landmark graphs and Q is the total number of edges.... In PAGE 9: ... This involves a post-processing step, where the graph V0 is grown in size after each new image is aligned. This is an O(F) operation, see Table1 . Growing V0 in an on-line fashion would permit extended regions of surface data to be incorporated into a single contiguous data set.... ..."

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