### 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 10: Complexity of computing the minimal domains in tractable augmented qualitative networks. discrete domains, we shall keep two pointers, Inf and Sup, to inf(Di) = v1 and sup(Di) = vk, respectively. We shall use three parameters in analyzing the computational complexity of algorithms: n|the number of nodes in the network, e|the number of arcs, and k|the maximum domain size, that is, the number of values in a domain (for discrete domains) or the number of intervals per domain (for continuous domains). In the rest of this section we show that for augmented CPA networks and for some augmented PA networks, the interesting tasks can be solved in polynomial time using local consistency algorithms such as arc consistency (AC) and path consistency (PC).

1991

Cited by 132

### Table 10: Complexity of computing the minimal domains in tractable augmented qualitative networks. discrete domains, we shall keep two pointers, Inf and Sup, to inf(Di) = v1 and sup(Di) = vk, respectively. We shall use three parameters in analyzing the computational complexity of algorithms: n|the number of nodes in the network, e|the number of arcs, and k|the maximum domain size, that is, the number of values in a domain (for discrete domains) or the number of intervals per domain (for continuous domains). In the rest of this section we show that for augmented CPA networks and for some augmented PA networks, the interesting tasks can be solved in polynomial time using local consistency algorithms such as arc consistency (AC) and path consistency (PC).

1991

Cited by 132

### Table 6. Computational time for various size problems * Normalized by case #1

1984

"... In PAGE 14: ... Since for our proposed formulation, m is always much greater than n the chance of exponential increase for computational time for solving simplex algorithm is small [5]. Using the worst computational time from Table6 and assuming k=1 (a worst case) on the running term O(lk), the solution time will be less than 27 seconds. This detailed analysis shows clearly the computational tractability of the protection design problem.... ..."

Cited by 1

### Table 7: Per-client mean latencies (in ms) for multi-client DB2. Latencies are computed using equations 2 and 3 with Ta = 0.2 ms and Td = 5 ms. Speedups over NONE-LRU, and the geometric mean of all client speedups, are also shown. ghost caches. To do so, we assigned the value 0 to represent the head of the real array LRU queue, and the value 1 to the tail; the insertion points for demoted and disk-read blocks were given by the ratio of the hit rates seen by their respective ghost caches to the total hit rate across all ghost caches. To make insertion at an arbitrary point more computationally tractable, we approximated this by dividing the real array LRU queue into a fixed number of segments Nsegs (10 in our experiments), multiplying the calculated insertion point by Nsegs, and inserting the block at the tail of that segment. We experimented with uniform segments, and with exponential segments (each segment was twice the size of the preceding one, the smallest being at the head of the array LRU queue). The same segment-index calculation was used for both schemes, causing the scheme with segments of exponential size to give significantly shorter lifetimes to blocks predicted to be less popular. We designated the combination of demotions with ghost caches and uniform segments at the array as DEMOTE- -ADAPT-UNI, and that of demotions with ghost caches and exponential segments as DEMOTE-ADAPT-EXP. We then re-ran the experiments for which we had data for multiple clients, but separated out the individual clients.

2002

Cited by 69

### Table 1: Summary of theoretical results for D-SEPs. The last two columns show the time complexity of nding the optimal policy for a D-SEP with N participants. In general, this problem is EXPTIME-hard but if the utility function is K-partitionable then the problem is polynomial time in N. Adding restrictions on how often the manager may send suggestions makes the problem even more tractable. Note that the size of the optimal policy is nite and must be computed only once, even though the execution of a SEP may be in nite (e.g., with AnyUnlimited ).

"... In PAGE 7: ... Thus, the optimal policy may be computed via a depth- rst search over the graph in total time O(N3K). 2 Table1 summarizes the results presented above as well as a few other interesting cases ( Immediate and Synchronous ). These results rely on two key optimizations.... ..."

### Table 1: Summary of theoretical results for D-SEPs. The last two columns show the time complexity of nding the optimal policy for a D-SEP with N participants. In general, this problem is EXPTIME-hard but if the utility function is K-partitionable then the problem is polynomial time in N. Adding restrictions on how often the manager may send suggestions makes the problem even more tractable. Note that the size of the optimal policy is nite and must be computed only once, even though the execution of a SEP may be in nite (e.g., with AnyUnlimited ).

"... In PAGE 7: ... Thus, the optimal policy may be computed via a depth- rst search over the graph in total time O(N3K). 2 Table1 summarizes the results presented above as well as a few other interesting cases ( Immediate and Synchronous ). These results rely on two key optimizations.... ..."

### Table 1 depicts the condition number of B as a function of the B-spline degree n. We observe a moderate increase with n making the problem tractable for all spline orders used in practice.

"... In PAGE 5: ... 1 As a consequence the eigenvalues of B can be computed at the speed of DFT algorithms. Table1 . Condition number of B as a function of the degree n of the B-spline degree n condition number 2 2.... ..."

### Table 2. A list of counting constraints that are intractable to propagate with GAC.

2004

"... In PAGE 5: ... We use the basic tools of computational complexity to show their tractability or intractability. Table2 gives some of the intractability results we obtained for counting constraints on integer variables. Proofs are in [3].... ..."

Cited by 7