### Table 4: Resultsb

"... In PAGE 17: ... The solver has been built on top of a finite-domain constraint solver [5] which itself is part of a constraint-logic programming environment [8]. Table4 reports the percentage of solved and decided problems out of 1000. Runs were constrained to abort after 1000 dead ends.... ..."

### Table 2: Results for benchmarks using a CHR min solver extending a finite domain solver.

2003

"... In PAGE 11: ... We use four versions of the CHR code, the base ver- sion uses simple lists to store CHR constraints and rechecks each rule whenever a variables domain changes (as in Ex- ample 8), spec specializes the re-execution (as described in Example 12), tree uses tree indexes (implemented as in Ex- ample 25) and both does both. The results in Table2 show that specialization is very important when there are no in- dexes available. Even when there are no partners to try to join with re-execution, specialization improves around 30%.... ..."

Cited by 6

### Table 2: Results for benchmarks using a CHR min solver extending a finite domain solver.

2003

"... In PAGE 11: ... We use four versions of the CHR code, the base ver- sion uses simple lists to store CHR constraints and rechecks each rule whenever a variables domain changes (as in Ex- ample 8), spec specializes the re-execution (as described in Example 12), tree uses tree indexes (implemented as in Ex- ample 25) and both does both. The results in Table2 show that specialization is very important when there are no in- dexes available. Even when there are no partners to try to join with re-execution, specialization improves around 30%.... ..."

Cited by 6

### Table 1. Testing ask constraints: (a) Boolean benchmarks, (b) Sequence benchmarks

2004

"... In PAGE 12: ... We believe an optimizing ask constraint compiler could translate equals to nonvar automatically. Table1 (a) compares the execution times in milliseconds of the Boolean solvers on a test suite (details explained in [2]). Most of the overhead of non- var compared to hand is due to the nonvar code retesting the nonvar ask-test... In PAGE 13: ... The equals version adds overhead with respect to nonvar by using a greater number of (more specialised) ask constraints. Our second experiment, shown in Table1 (b)), compares two versions of a sequence (Herbrand lists of finite domain integers) solver built using both a Her- brand solver for lists, and a finite domain (bounds propagation) solver. The re- sulting sequence solver provides three ask constraints over complex structures: length(Xs,L) (see Example 4), append(Xs,Ys,Zs) which constrains Zs to be the result of appending Xs and Ys (concatenation constraint), and neq(Xs,Ys) (see Example 5).... ..."

Cited by 1

### Table 1: Overview of constraints and solvers in interactive graphical applications.

1998

"... In PAGE 2: ... For each application, I highlight the unique and interesting features of the system while listing the class of constraints it handles. For an overview of the kinds of constraints supported by each system, the solving technique employed, and the performance of the solver, see Table1 . Most notably, this section will show that applications tend to pollute their use of constraints based on limitations of the underlying solver.... In PAGE 8: ... Badros 2.6 Summary of application domains As Table1 shows, constraints used by di erent systems within an application domain are generally not especially closely related. The similarities that do exist result more from the underlying solver than from the needs of a particular class of applications (see the following section).... In PAGE 29: ... This paper surveys several interactive graphical application domains that use constraint sys- tems. Table1 shows that several kinds of constraints are especially relevant for geometric applica- tions, but that the constraints provided by an application are highly influenced and restricted by its underlying solver. Thus, increasing expressiveness of constraint solvers is a primary concern.... ..."

Cited by 1

### Table 2. Characteristics of the solvers on di erent HSPs The CLP solver:

1998

"... In PAGE 11: ... Constraint handling is performed by constraint propagation on nite domains and linear constraint solving. 5 Empirical Results Let us discuss the empirical results of the hybrid CLP amp;MIP solver relative to the results of the CLP and MIP solvers on the following HSPs from Section 2: The empirical results in Table2 show that HSPs are hard for our CLP solver.... In PAGE 13: ... Since constraint propagation is performed before linear constraint solving it is di cult to say which procedure is more important. All timings in Table2 are in CPU seconds running on a SUN-SPARC/20. quot;FD-fails quot; denotes the number of failures by performing constraint propagation and quot;LP-fails quot; denotes the number of failures by linear constraint solving.... ..."

Cited by 12

### Table 1.B: Benchmark Results for a Finite Difference Time Domain Application

"... In PAGE 6: ...ables 1.A to 1.D are some of the results of benchmarks performed at the Cal- ifornia Institute of Technology showing that the Beowulf architecture provides a new operating point in performance to cost for high performance workstations.[11] Naegling T3D T3E600 CPU Speed (MHz) 200 150 300 Peak Rate (MFlops) 200 300 600 Memory(MB) 128 64 128 Comm Latency 322 35 18 Comm Throughput 78 225 1200 Cost 154000 500000 750000 Table1 .A: Setup For Benchmark Testing at the California Institute of Technology Naegling is a 120 node Pentium Pro cluster built at the Center for Computing Research at the California Institute of Technology.... In PAGE 6: ... Table1 .C: Benchmark Results for a Physical Optics Application Number of Processors Naegling T3D T3E600 1 6.... In PAGE 6: ...7 9.6 Table1 .D: Benchmark Results for a Incompressible Fluid Flow Solver From the above data, it is clear in most cases the Beowulf machine out-performs the T3D machine.... ..."

### Table 6: Multiple Constraint Solvers

"... In PAGE 9: ...III.D. Multiple Constraint Managers in an Architecture An issue related to using multiple constraint managers inside a single component is using multiple constraint man- agers in different components, but in a single architecture. Such an architecture was built using components shown in Table6 . In this architecture, Palette Boundary and Resizing constraints are maintained by SkyBlue, and Palette Location and Tile Location by Amulet.... ..."

### lable constraints to denote small finite candidate sets

1998

Cited by 1

### Table 4: An example of constraint solving on the domain Colour Ch.P. C

"... In PAGE 22: ... The choice points are introduced by the de nition of the propagator 6 =0. Table 3 also gives the interval constraints used by Table4 to show the constraint solving process. Three choice points are added by the inference machine and backtracking is executed when an inconsistency or a solution is found by the generic solver.... ..."