### Table 1: Asymptotic degree-diameter properties of the difierent graphs.

in Graph-Theoretic Analysis of Structured Peer-to-Peer Systems: Routing Distances and Fault Resilience

2003

"... In PAGE 4: ... As we show in section 7, distributed de Bruijn graphs possess no more conceptual complexity than Chord, achieve optimal diameter in the peer-to-peer graph, and can be built with a flxed application-layer degree. Table1 shows asymptotic diameter and node degree of de Bruijn graphs and several existing (deterministic) struc- tures. First note that we assume that CAN uses circular (toroidal) routing in each of the dimensions, which means that all nodes along the borders maintain 2d neighbors and that the CAN graph is regular.... ..."

Cited by 68

### Table 1: Summary of Results for -SAT(S).

1995

"... In PAGE 5: ...2 Applications Theorem 6.6 characterizing the complexity of succinctly specified generalized CNF satisfiability prob- lems can be used to prove both hardness/easiness results for succinctly specified logic and graph prob- lems (see Table1 and 2 for examples of such problems). For instance, first, the results imply the PSPACE-hardness of the problems 1-FPN(BC)-MCVP, 1-FPN(BC)-AGAP,8 L-MCVP and L-AGAP for O(log N ) bandwidth-bounded instances9.... In PAGE 33: ... We formalize some of these issues in a related paper [HSM97]. The results characterizing the complexity of succinctly specified satisfiability problems is summa- rized in Table1 . The complexity of various succinctly represented graph and combinatorial problems can be obtained using our results for satisfiability problems.... ..."

Cited by 6

### Table 2: The order of the largest known graphs of maximum degree and diameter D.

2005

"... In PAGE 16: ...Table2 shows a summary of current largest known graphs for degree 16 and diameter D 10. These graphs provide the best current lower bounds on the order of graphs for given values of degree and diameter.... In PAGE 16: ...fr quot;. Recent updates in Table2 are due to Exoo: entries (3,6)-(3,8), (4,4), (4,7), (5,3), (5,5), (6,3), (6,4), (7,3), (16,2); to Hafner: entries (5,9), (5,10), (6,7)-(6,10), (7,6)-(7,10), (8,5), (8,7), (8,9), (8,10), (9,7), (9,10), (10,5), (10,7)-(10,10), (11,5), (11,7), (11,8), (12,7), (13,5), (13,7), (13,8), (14,5), (14,8), (15,8); to Quisquater: entries (3,9), (3,10); to G omez and Pelayo: entries (5,6), (6,6), (8,6), (9,6), (10,6), (12,6), (14,9); to Sampels: entries (4,8), (4,10), (5,8)-(5,10), (6,7)-(6,10), (7,6)-(7,10), (8,8)-(8,10), (9,4), (9,5), (9,8)-(9,10), (10,5), (10,7), (10,8)-(10,10); to McKay, Miller, Sir a n: entries (11,2), (13,2); and to G omez: entries (5,6), (8,6), (9,6), (10,6), (12,6), (14,6) [89]. 2.... In PAGE 18: ... The survey emphasises algebraic features, such as cosets, conjugacy classes, and automorphism actions, in the determination of some topological properties of over 18 types of networks. We note that roughly one half of the values in Table2 have been obtained from Cayley graphs. Computer-assisted constructions of large ( ;D)-graphs, for relatively small and D, from Cayley graphs of semidirect products of (mostly cyclic) groups can be found in Hafner [155].... ..."

Cited by 7

### Table 2: Comparison of existing tools with mAETG SAT and SA SAT

"... In PAGE 10: ...66. Table2 shows size data on computed CIT samples for a selec- tion of the data we collected (the other results are similar). For each of the CCAs we give the unconstrained array first (F ={}), followed by its constrained counterpart.... In PAGE 10: ... They produce the smallest size arrays and are applicable for higher strength. The examples in Table2 are relatively small. To validate our algorithmic extension on larger realistic examples we use the SPIN and GCC models described in the case study.... ..."

### Table 1. Graphs and some of their properties used in the experiments.

2004

"... In PAGE 10: ...g. a small vertex degree and diameter and large connectivity, as Table1 displays. Furthermore, we also include Ramanujan (RAMAN) graphs that are described in [15].... In PAGE 12: .... However, what cannot be seen is that with values close to 1 the convergence rate decreases again. As seen from the experiments on the torus, the parameters p, SS/RS and c do affect the convergence rate of both algorithms, but comparing the differences between the constant and the dynamic approach, the situation is always very similar. Therefore, we restrict the presentation of the results for the other graphs listed in Table1 to the settings p = 0.... ..."

Cited by 4

### Table 1: Notation in the Moore-Greitzer model

"... In PAGE 13: ...heorem 5.2 Under the conditions of Theorem 5.1, there exists a unique exponentially sta- ble periodic solution of (11){(14) in an O(! + + a)-neighborhood of the point x ; ^ ; ; = (l( ) ; ; 0 ; h l( )). 6 Application to a Compressor Model We now apply the peak seeking scheme of Section 3 to the Moore-Greitzer compressor model [25]: _ R = 3 pR Z 2 0 C + 2pR sin sin d (54) _ = ? + 1 2 Z 2 0 C + 2pR sin sin d (55) _ = 1 2 ( ? T) ; (56) where the quantities are de ned in Table1 , and the initial condition of the state R = A2 4 is physically restricted to be nonnegative, R(0) 0. The throttle ow T is related to the pressure rise through the throttle characteristic = 1 2 (1 + C0 + T)2 ; (57)... ..."

### Table 1. Graphs and some of their properties used in the experiments.

2004

"... In PAGE 8: ...g. a small vertex degree and diameter and large connectivity, as Table1 displays. Furthermore, we also include Ramanujan (RAMAN) graphs that are described in [15].... In PAGE 10: .... However, what cannot be seen is that with values close to 1 the convergence rate decreases again. As seen from the experiments on the torus, the parameters p, SS/RS and c do affect the convergence rate of both algorithms, but comparing the differences between the constant and the dynamic approach, the situation is always very similar. Therefore, we restrict the presentation of the results for the other graphs listed in Table1 to the settings p BP 0BM5, SS and c BP 1BM1. Figures 7 through 14 show the details.... ..."

Cited by 4

### Table 1. The set of PNE for S = 2. DNE stands for does not exist, implying the non- existence of pure strategy Nash equilibria, although the existence of mixed strategy equilibria is established in Nash [28].

### Table 12. Existing Force Design Tools

1999

"... In PAGE 9: ...able 11. OOTW mission planning complaints ................................... 16 Table12 .... In PAGE 37: ... The Force Facilitator For Operations Other Than War (FFFOOTW) was also not discussed at the workshop, but is reputed to be force design tool for OOTW. Table12 summarizes some pertinent observations concerning these tools that were gleaned from the presentations. The column labeled quot;Positives quot; represents features that satisfy some part of an quot;ideal quot; force design tool, a joint/combined, complete, easy to use, and OOTW oriented tool (more... In PAGE 38: ...hort of the ideal. The quot;Mitigation quot; column indicates the effort required to improve a quot;negative quot; area. Shaded cells indicate especially significant comments. Table12 . Existing Force Design Tools TOOL POSITIVES NEGATIVES MITIGATION CAPS has structure to aid in deciding which units to use does not have actual forces in structure requires programming amp; data has internal help facility does not allow for coalition or NGO/PVO contribution to effort requires minor programming host nation support can offset US support does not allow for time phasing requires programming workloads by UJTL does not have data on transportation or logistics requirements for units requires minor programming and data collection units have capacity to do work limited task set requires data collection and cross referencing security forces can be planned no data maintenance utilities requires major programming allows modification of previous plans limited mission types requires data collection good base to build force design tool limited user input to design FA amp;CT relates tasks to actual Army units (converts SRC to Unit Identification Code (UIC)) current data Army only requires major programming can allocate future forces accumulates for multiple OOTWs FALCON computes tempo amp; resource stress analysis, support requirements, force allocations amp; mix/sizing Air Force orientation requires major programming has rules for reconstitution requirements Tactical Air (TacAir) orientation requires data accumulates for multiple OOTWs scheduling orientation FAST-OR has extensive data about Standard Requirements Code (SRC) units has only partial structure to aid in deciding which units to use (built- in Army assumptions) requires major programming to go beyond assumptions has documentation data are basically Army only requires data collection and analysis host nation support can offset US support enforces Army doctrine Army allocation rules are no longer current requires major programming permits support to other Services, refugees amp; allied forces doesn apos;t deal with Active vs Reserve unit availability or readiness (equipment or personnel) requires major programming extensive allocation rules for units implied by workloads, including HQ units amp; tailored sizes no connection to non-military command and control (C2) contains Army doctrine FAST-OR allows manual creation of time phases for when units are needed not a good base from which to build operational tool FFFOOTW automated tool to determine force structure requirements for OOTW no personal knowledge of tool JEB generates needs assessment using included planning factors does not have structure to aid in deciding which units to use... ..."