### Table 1: The maximal tractable subalgebras of RCC-5.

"... In PAGE 6: ...XfDRgY i X \ Y = ? XfPOgY i 9a; b; c : a 2 X; a 62 Y; b 2 X; b 2 Y; c 62 X; c 2 Y XfPPgY i X Y XfPPIgY i X Y XfEQgY i X = Y Table1 : The ve basic relations of RCC-5. Y X X Y X Y Y X X Y DR(X; Y ) PO(X; Y ) PP(X; Y ) PPI(X; Y ) EQ(X; Y ) Figure 1: Pictorial example of the relations in RCC-5.... ..."

### Table 2: The maximal tractable subalgebras of RCC-5.

### Table 1: Tractable classes of the point algebra for partially ordered time [5].

"... In PAGE 19: ... xky i neither x y nor y x The point algebra for partially ordered time has been throughly investigated earlier and a total classi cation with respect to tractability has been given in Broxvall and Jonsson [4]. In Broxvall and Jonsson [5] the sets of relations in Table1 are de ned and it is proven that ?A _ A, ?B _ B, ?C _ C and D are the unique maximal tractable disjunctive classes of relations for partially ordered time. The proofs of tractability for those sets relied on a series of handmade independence proofs.... ..."

### Table 2: The maximal tractable subalgebras of RCC-5. Theorem 3.4 RSAT(R17 5 ) is polynomial.

1997

Cited by 27

### Table 1: Tractable classes

2000

"... In PAGE 3: ... 2 Tractability Results We continue by defining four classes of disjunctive relations TA; : : : ; TD and show that their corresponding satisfiabil- ity problems are tractable. The classes are defined as fol- lows: TA = ?A _ A, TB = ?B _ B, TC = ?C _ C and TD = D and the exact definitions of the sets of relations can be found in Table1 . The classes TA and TB are exten- sions of the algebras A14 and A10 as defined by Broxvall and Jonsson (1999).... ..."

Cited by 3

### Table 1: Tractable classes

"... In PAGE 3: ... 2 Tractability Results We continue by defining four classes of disjunctive relations T A ;:::;T D and show that their corresponding satisfiabil- ity problems are tractable. The classes are defined as fol- lows: T A = , A #02 _#01 #03 A , T B = , B #02 _#01 #03 B , T C = , C #02 _#01 #03 C and T D =#01 #03 D and the exact definitions of the sets of relations can be found in Table1 . The classes T A and T B are exten- sions of the algebras A 14 and A 10 as defined by Broxvall and Jonsson (1999).... ..."

### Table 1: The thirteen basic relations. The endpoint relations x? lt; x+ and y? lt; y+ that are valid for all relations have been omitted. and metric reasoning, together with the satis ability algorithm, and Section 4 presents the new maximal tractable algebras, and how to provide these with metric temporal information. In Section 5 and Section 6, we prove that the algorithm is correct, and that the algebras are maximal. Finally, Section 7 and Section 8 discuss and conclude the paper.

1997

"... In PAGE 4: ...e. the endpoint relations required by r (see Table1 ) are satis ed by the assignments of u and v. Then M is said to be a model of hV; Ei.... ..."

Cited by 22

### Table 1. Tractability of symmetry breaking and dominance detection

"... In PAGE 35: ... Unfortunately, efficient symmetry breaking by such dominance-detection schemes has its limits, as we have identified some CSP classes where dominance detection is intractable. Table1 summarizes our main results, where P (Thm i) means that breaking all the symmetries mentioned in the corresponding row is feasible with a poly- nomial overhead with respect to both time and space at every node explored for the corresponding (set-) CSP in the column, as proved in Theorem i. Some of these positive tractability results, namely the ones marked P (from Thm i) , are trivially derivable as consequences from Theorem i.... ..."

Cited by 1