Resource Allocation in Communication Networks Using Abstraction and Constraint Satisfaction

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Resource Allocation in Communication Networks
Using Abstraction and Constraint Satisfaction

• C. Frei, B. Faltings and M. Hamdi
• ABB, EPFL and HK U. of Science and Tech.
• IEEE JSAC, Feb. 2005

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Outline (1/2)

• Introduction
• Resource Allocation in Network (RAIN)
• Problem Model
• Constraint Satisfaction Problem (CSP)
• Problem Solving in CSP
• Blocking Island (BI) Paradigm
• BI Clustering Scheme
• Problem Model

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Outline (2/2)

• CSP Problem Solving in BI
• Empirical Results

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Introduction

• The goal of QoS Routing
• To achieve global efficiency in network resource
  utilization.
• To satisfy the QoS requirements of each admitted
  connection.
• QoS Path Placement with Single constraint is a
  NP-complete Problem. (Ex BW)
• QoS Path Placement with Multiple constraints is a
  NP-Hard Problem. (Ex E2E delay loss rate)

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Resource Allocation in Network

• Simple Analysis
• A complete network has N nodes.
• The length of route is bounded by N-1
• A routes length j has j-1 intermediate nodes
  between Source and Destination.
• The number of routes of length j is(N-2)! /
  (N-j-1)! (???node)

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RAIN (cont.)

• The total number of routes between any pair of
  nodes is
• A complete graph with 10 nodes, there are 69281
  routes between any pair of nodes.

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Uninformed Search
Criterion Time Space Optimal
BFS b(d1) b(d1)
DFS bm bm
Depth-Limit bl bl
b max branching factor of search tree. d
depth of the tree. m max depth of tree.
(bound) l limited depth
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Complete Algorithm

• Completeness The algorithm guaranteed to find a
  solution.
• Shortest Path method is a incomplete algorithm.
• There is a need for heuristics to guide the
  search, in order to solve most problem in a
  reasonable amount of time.

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Constraint Satisfaction Problem

• Define
• A triple (X, D, C), where X x1, x2, ,xn
  is a set of variables, D D1, D2, , Dn is a
  set of finite domains associated with the
  variables, C C1, C2, , Cn is a set of
  constraint.
• The domain of a variable is the set of all
  values that can be assigned to that variable.

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CSP (cont.)

• Example Map Coloring

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CSP (cont.)
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Problem Solving in CSP

• Backtracking (BT)
• Variable and value ordering
• Minimum Remaining Values heuristic (MRV)
• Degree heuristic
• Least-constraining-value
• Forward Checking (FC)
• Backjumping (BJ)

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BT and BJ

• BT is used for a DFS that choose values for one
  variable at a time and backtracks when a variable
  has no legal values left to assign.
• BJ is the method backtracks to the most recent
  variable in the conflict set.
• The conflict set is a set of variables that
  caused the failure.

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BT / BJ Example
WA
NT
Q
??????assign NSW, ???R,G, ???assign
SA. ??jump?Q, ??assign
SA no solution
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Variable and Value Ordering

• Variable ???????????assign
• Value ??????????assign
• Minimum Remaining Values heuristic (MRV)
• Choosing the variable with the fewest legal
  values

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Variable and value ordering (cont.)

• Degree heuristic
• To reduce the branching factor on future choices
  by selecting the variable that is involved in the
  largest number of constraints on other unassigned
  variables
• Least-constraining-value
• It prefers the value that rules out the fewest
  choices for the neighboring variables in the
  constraint graph.

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Forward Checking

• Whenever a variable X is assigned, the forward
  checking process looks at each unassigned
  variable Y that is connected to X by a constraint
  and deletes from Ys domain any value that is
  inconsistent with the value chosen for X.

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Min-Conflicts
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Comparison of various CSP
Problem BT BTMRV FC FCMRV Min-Conflicts
USA (4-color) gt 1M gt 1M 2K 60 64
N-Queens(250) gt 40M 13,500K gt40M 817K 4K
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Blocking Island (BI) Paradigm
BIH BI hierarchy
BIG BI Graph
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Blocking Island (BI)

• A ß-blocking island (ß-BI) for a node x is the
  set of all nodes of the network that can be
  reached from x using links with at least
  ßavailable resources, including x.

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BI (cont.)

• The BIs partition the network into equivalence
  classes of nodes.
• The BIs are unique and identify global
  bottlenecks.
• The splitting and merging BIs.

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BIH
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BIH (cont.)

• ß-BI can be obtained by simple greedy algorithm,
  with a linear complexity of O(m), where m is the
  number of links.
• BIH is obtained by recursive calls to BIG
  computation algorithm. The time complexity is
  bounded in O(bm), where b is the number of
  possible bandwidth requirement.

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Routing Problem Model

• A single demand du(c, e, 16K).

• Lowest level (LL) heuristic
• Not route to other clusters
• Lr c -gt b -gt d -gt e
• In the Lower BI, there are less critical links
  clustered in it.

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Routing Problem Model (cont.)

• Route selection in BI
• Minimal splitting (MS)
• Cause the fewest splitting of BIs I the BIH.
• More splittings, more critical links
• Shortest-widest path (WP)
• Not good

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Routing Problem Model (cont.)
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CSP Problem Solving in BI

• FC
• Value Ordering
• LL heuristic
• Variable Ordering
• Dynamic Variable Ordering Highest Level (DVO-H)
• Dynamic Variable Ordering Numver Level (DVO-N)
• Min-Conflict
• Reroute conflict path with BJ

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DVO

• DOV-H
• First choose the demand whose lowest common
  father of its endpoint is the highest n the BIH.
  ( highest BIH means low in resource requirement
  and more routes constraints)
• DOV-N
• First choose the demand for which the difference
  in number of levels (in the BIH) between the
  lowest common father of its endpoint and
  resources requirements is lowest.

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Empirical Results

• Compared Algorithms
• Shortest Path Algorithm (SP)
• Shortest Path with Backtracking (BT-SP)
• BI with LL heuristic and DVO-HL (BI-LL-HL)
• BI with LL heuristic and DVO-NL (BI-LL-NL)
• BI-LL-HL with Backjumping (BI-BJ-LL-HL)
• BI-BJ-LL-NL

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Empirical Results (cont.)

• Tightness is defined as the ratio of resources
  required for the best possible allocation (in
  terms of used bandwidth) divided by the total
  amount of resources available in the network.

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Empirical Results A

• Simulation-A Environment (feasible)
• Find a feasible solution
• 23,000 runs.
• Each run has a random topology of 20 nodes, 38
  links and 80 demands.
• Each demand characterized by two endpoints and a
  bandwidth constraint.
• A solution must allocate all demands within the
  bandwidth constraint.

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Results A-1
Run Time lt 1s
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Results A-2
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Empirical Results B

• Simulation-B Environment (feasible)
• Find a feasible solution
• 6000 runs.
• Each run has a random topology of 38 nodes, 107
  links and 1200 demands.
• Each demand characterized by two endpoints and a
  bandwidth constraint.
• A solution must allocate all demands within the
  bandwidth constraint.

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Results B-1
NL??Traffic??cluster?
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Empirical Results C

• Simulation-C Environment (feasible)
• Find a feasible solution
• 50 nodes, 171 links and 3000 demands.
• BI-BJ-LL-NL solved it in 4.5 min
• BT-SP was not able to solve it with in 12 hour.
• 1600?

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Empirical Results C

• Simulation-C1 Environment (infeasible)
• Find a feasible solution
• 300 runs.
• FUDI topology. (Europe Topology 12 nodes, 14
  links, BW 634Mb/s)
• Demand of each run 2024
• BW of Demand uniformly distributed in 510Mb/s

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Empirical Results C (cont.)

• Simulation-C2 Environment (infeasible)
• Find a feasible solution
• 300 runs.
• FUDI topology. (Europe Topology 12 nodes, 14
  links, BW 634MB)
• Demand of each run 78 164
• BW of Demand uniformly distributed in 0.05, 0.1,
  0.2, 0.3, , 0.9, 1.0

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Results C-1
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Results C-2
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Conclusion

• Using BI abstractions coupled with CSP can solve
  the network bandwidth allocation problem in
  reasonable time with a complete search algorithm.
• This method gives better solutions than Shortest
  Path routing algorithms.