terminal assignment algorithms

1. Terminal Assignment and
concentrator location
Presented by-kamalakshi Deshmukh
M.E(Comp)
Roll No-ME101
Guided by- Prof.Rahul Dagade
Marathwada Mitra Mandal College of Engineering(MMCOE) PUNE

2. Centralized Network Design
 Centralized network: is where all communication is
to and from a single central site
 The “central site” is capable of making routing
decisions
→ Tree topology provides only one path through the
center
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Center
Concentrator Concentrator
Terminal Terminal Terminal Terminal
High speed lines
Low speed lines

3. Outline
 Topology Design for Centralized Networks
 Multipoint Line Topology
 Terminal Assignment
 Concentrator Location
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4. Centralized Network Design
Problems
 Multipoint line topology: selection of links connecting
terminals to concentrators or directly to the center
 Terminal assignment: association of terminals with
specific concentrators
 Concentrator location: deciding where to place
concentrators, and whether or not to use them at all
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5. Terminal Assignment
 Greedy Algorithm
 Modified Greedy Algorithm
 Alternating Chain Algorithm or Exchange Algorithm
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6. Terminal assignment - Problem
Statement
 Terminal Assignment: Association of terminals with specific concentrators
 Given:
 T terminals (stations) i = 1, 2, …, T
 C concentrators (hubs/switches) j = 1, 2, …, C
 Cij: cost of connecting terminal i to concentrator j
 Wj: capacity of concentrator j
 Assume that terminal i requires Wi units of a concentrator capacity
 Assume that the cost of all concentrators is the same
 xij = 1; if terminal i is assigned to concentrator j
 xij = 0; otherwise
 Objective:
 Minimize:
 Subject to:
i = 1, 2, …, T (Each terminal associated with one Concentrator)
j = 1, 2, …, C (Capacity of concentrators is not exceeded)
∑∑
= =
=
C
j
T
i
ijij xcZ
1 1
1
1
=∑
=
C
j
ijx
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j
T
i
iji wxw ≤∑
=1
}1,0{∈ijx

7. Greedy Algorithm
 It is based on the following observations:
 The basic idea of this algorithm is to assign every terminal to the
nearest concentrator. (In the absence of the capacity constraint on
concentrators)
 In constraint case it is possibility that some terminals cannot be assigned
to the nearest concentrators. This algorithm will assign each terminal to
the "best available" concentrator.
 The terminal to be assigned first is the one with the smallest connection
cost overall and followed by the one with the second smallest cost , the
third smallest cost and so on. subject to the capacity constraint of every
concentrator.
 This process continues until all terminals have been assigned or the
algorithm fails to find a feasible solution.
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8. Cont.. Example
 20 terminals each of 3 wt, and 6 concentrator (10
capacity)
 Total weight is 60 = total capacity
No way to assign 10 units to each concentrator
 Algorithm fail to find one
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9. Modified Greedy Algorithm
 The purpose of this modification is to give preference to
the terminals that would suffer the most by not being
connected to the nearest concentrators.(critical
terminals)
 Instead of using the connection cost as a criterion in
choosing the order of assignments a tradeoff function that
reflects this preference is used.
 ti = Cil - αCi2
 Where cil is the cost of connecting terminal i to the first
best available concentrator
 Ci2 is the cost of connecting terminal i to the second best
available concentrator.
 where α is a parameter between O and 1,
 α is 0 then there is no preference and algorithm work like
original greedy algorithm
 And 1 when preference is given to the critical terminal
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10. Exchange or alternating chain
Algorithms
 Cij +Ckm > Cim + Cjk (exchange assignment of pair of
terminals))
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J m
k i

11. Exchange or alternating chain
Algorithms
 All terminals should be assigned to their nearest best
concentrators, except if the capacity constraints
would be violated.
 A terminal that has already been assigned to its best
concentrator can be moved to another concentrator
only if it will create room for another terminal which
otherwise would have deviated farther.
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12. Concentrator
Location

13. Concentrator location - Problem
Statement Concentrator location: deciding where to place concentrators, and whether or not to use them at all
 Given:
 T terminals (stations) i = 1, 2, …, T
 C concentrators (hubs/switches) j = 1, 2, …, C
 Cij: cost of connecting terminal i to concentrator j
 dj: cost of placing a concentrator at location j (i.e., cost of opening a location j)
 Kj: maximum capacity (of terminals) that can be handled at possible location j
 Assume that terminal i requires Wi units of a concentrator capacity
 xij = 1; if terminal i is assigned to concentrator j; 0, otherwise
 yj = 1; if a concentrator is decided to be located at site j; 0, otherwise
 Objective:
 Minimize:
 Subject to:
i = 1, 2, …, T (Each terminal associated with one Concentrator)
j = 1, 2, …, C (Capacity of concentrators is not exceeded)
∑∑∑
== =
+=
C
j
jj
C
j
T
i
ijij ydxcZ
11 1
1
1
=∑
=
C
j
ijx
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jj
T
i
iji yKxw ≤∑=1
}1,0{, ∈jij yx

14. COM algorithm
 The basic idea of this algorithm is to identify the
natural cluster of traffic.
 One starts by assuming that each terminal is in a cluster
by itself, and then creates a new cluster by combining
two clusters that are close to each other subject to
some given constraints.
 Let us assume that for each terminal i, we have its
coordinates, (xi,yi), and weight, wi.
 If terminals i and j are to be combined, then a new
cluster formed with these two terminals is represented
by their enter of mass, (xk,yk), which can be calculated
as follows:
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15. Concentrator location - Add
Algorithm
 Greedy Algorithm
 Start with all terminals connected directly to the center
 Evaluate the savings obtainable by adding a
concentrator at each site
 Greedily select the concentrator which saves the most
money
 This algorithm stops when the addition of a new
concentrator will not result in any savings.
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16. Cont.. ADD Algorithm
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17. Concentrator location - DROP
 Reverse direction of the ADD algorithm.
 At the beginning all possible sites of concentrators are
considered in use.(no capacity constraint)
 The algorithm then investigates each concentrator to
find out which one will bring the most savings if it is
dropped the configuration.
 The algorithm stops if it no longer finds a concentrator
whose removal will save some money.
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18. References
 A. Kershenbaum, “Telecommunications
Network Design Algorithms”, McGraw-
Hill,1993
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19. Thank you !
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