Tributaries and deltas efficient and robust aggregation in sensor networks
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Tributaries and Deltas: Efficient and Robust Aggregation in Sensor Networks. ManJhi, S. Nath P. Gibbons CMU. Introduction. Existing approaches to in-network aggregation: Tree –based approach Answer is generated by performing in-net aggregation along the tree

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Tributaries and Deltas: Efficient and Robust Aggregation in Sensor Networks

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Tributaries and deltas efficient and robust aggregation in sensor networks

Tributaries and Deltas: Efficient and Robust Aggregation in Sensor Networks

ManJhi, S. Nath P. Gibbons

CMU

ICS280sensors Winter 2005


Introduction

Introduction

  • Existing approaches to in-network aggregation:

    • Tree –based approach

      • Answer is generated by performing in-net aggregation along the tree

      • Proceed level by level from leaves

      • Exact computation

      • Suffer from high communication failures

        • “Not uncommon to loose 80% of readings”.

ICS280sensors, Winter 2005


Introduction1

Introduction

  • Multi-path approach

    • Use wireless broadcast medium

    • Broadcast partial results to multiple neighbors

    • Use topology called rings.

      • Nodes divided into levels according to hop count from BS

      • Aggregation performed level by level up to the BS.

    • Each reading is accounted for multiple times

      • Robust

    • Suffer from: approximate answers and long message size

ICS280sensors, Winter 2005


Approach comparison

Approach Comparison

ICS280sensors, Winter 2005


Tributary delta overview

Tributary-Delta overview

  • Combine the two approaches

  • Adapting the aggregation to the current loss rate

    • Low loss: trees are used

      • for low/zero approximate error and small size

    • High loss: multi-path

      • For robustness

ICS280sensors, Winter 2005


Challenges

Challenges

  • How do nodes decide whether to use tree or multi-path

  • How do the nodes using different approaches communicate

  • How do the nodes convert partial results when transitioning between approaches

  • New algorithm for finding frequent items

ICS280sensors, Winter 2005


More on multi path

More on multi-path

  • To construct a rings topology

    • BS transmits and any node hearing the transmission is in ring 1

    • Nodes in ring I transmit and any node hearing the transmission, but not already in a ring, is in ring I+1.

    • All level I nodes that hear a level i+1 partial result incorporate the result into its own result

    • Low communication error

ICS280sensors, Winter 2005


More on multi path1

More on multi-path

  • Special technique to avoid double-counting: synopsis (sketches) diffusion

    • Synopsis generation: takes a stream of local sensor readings at a node and produces a partial result-synopsis

    • Synopsis fusion: takes two synopses and generate a new one

    • Synopsis evaluation: translates a synopsis into a query answer

ICS280sensors, Winter 2005


More on multi path2

More on multi-path

  • Example: count distinct items

    • Let n by upper bound of the count

    • h() be a hash function from sensor ids to [1, … lg(n)]

    • SG function produces a bit vector of all 0’s and the sets the h(i)’th bit to 1 when see an id of i.

    • SF function is OR function

    • SE function takes a bit vector and output 2^(j-1)/0.77351, where j is the index of the lowest-order UNSET bit.

ICS280sensors, Winter 2005


Tributary delta

Tributary-Delta

  • View aggregation as a directed graph

    • Nodes and BS are vertices

    • Directed edge fro successful transmission

    • Vertex labeled either M or T, for multi-path or tree

    • Edge labeled based on source vertex

    • The labels may change

ICS280sensors, Winter 2005


Tributary delta1

Tributary-Delta

  • Correctness criteria of topology construction

    • No two M vertices with partial results representing an overlapping set of sensors are connected to T vertices.

  • Restrict to: a node receiving from an M node uses M scheme

  • Edge correctness: An M edge can never be incident on a T vertex

  • Path correctness: in any directed path in G, a T edge can never appear after an M edge

ICS280sensors, Winter 2005


Tributary delta2

Tributary-Delta

  • Dynamic adaptation:

    • An M vertex is switchable if all incoming edges are E edges, or no incoming edges (M1, M2)

    • A T vertex is switchable if its parent is an M vertex or it has no parent. (T3, T4, T5)

    • Let G’ be the connected component of G that includes the BS

    • “if the set of T vertices in G’ is not empty, at least one of them is switchable. If the set of M vertices in G’ is not empty, at least one of them is switchable”

ICS280sensors, Winter 2005


Adaptation design

Adaptation design

  • User specify a threshold on the minimum percentage of nodes that should contribute to the aggregate answer

  • Depending on the % of nodes contributing to the current result, the BS decides whether to shrink or expand the delta region for future result

    • Increasing delta region increases the % contributing

  • Key concern in switching nodes between tree and multi-path aggregation: transmitting and receiving synchronization

  • Design choice: (to ensure switched nodes can retain current epoch)

    • From M to T: must choose its parents from one of its neighbors in level i-1.

    • From T to M: transmits to all neighbors in level i-1

ICS280sensors, Winter 2005


Adaptation strategies

Adaptation strategies

  • TD-coarse: if the % is below the user-specified threshold, all the current switchable T nodes is switched.

  • TD:

    • each switchable M node includes in its outgoing messages an additional field : number of nodes in sub-tree not contributing.

    • Max and min of such number are maintained

    • If % is below threshold: BS expands the delta region by switching from T to M all children of swichable M nodes beloning to a sub-tree that has max nodes not contributing

    • When shrinking: switch each swichable M node whose subtree has only min nodes not contributing. ?

    • Trade-off: higher convergence time. (will it converge?)

ICS280sensors, Winter 2005


Identify frequent items

Identify frequent items

  • The problem:

    • Each of m sensor nodes generates a collection of items.

    • Given a user-supplied error tolerancee, the toal is to obtain from each item u, an e-deficient count c’(u) at the BS:

      • Max {0, c(u)-e*N} <= c’(u) <= c(u)

    • Where N = sum(c(u))

ICS280sensors, Winter 2005


Identify frequent items tree algorithm

Identify frequent items–tree algorithm

  • Partial result sent by a node X to its parent is a summary:

    • S = <N, e, {(u, c’(u))}>

    • Each c’(u) satisfies max {0, c(u)-e*N} <= c’(u) <= c(u)

  • Approach is to distribute the e among intermediate nodes in the tree.

    • Make e(i) a function of height of a node (height of a leaf node is 1)

    • For correctness: e(1)<= e(2) <=… <= e(h)

      • As long as e(h) <= e, user guarantee is met.

      • Called precision gradient

  • At each node: summary of items with count at most e*N is dropped.

ICS280sensors, Winter 2005


Identify frequent items tree algorithm1

Identify frequent items–tree algorithm

ICS280sensors, Winter 2005


Min total load algorithm

Min Total-Load algorithm

  • D-dominating tree: fro any d>=1, we say that a tree is d-dominating if for any i>=1,

    H(i)>=(d-1)/d*(1+1/d+…+1/d^(i-1))

    • Where H(i)=1/m*SUM(h(j)), with h(j) being the number of nodes at height j, and m the total number of nodes.

  • If a tree is d-dominating but not d+delta-dominating, refer to d as the domination factor.

ICS280sensors, Winter 2005


Min total load algorithm1

Min Total-Load algorithm

  • Lemma: for any d-dominating tree of m nodes, where d>1, a precision gradient setting of e(i)=e*(1-t)(1+t+…+t^(i-1)) with t=1/sqrt(d) limits total communication to (1+ 2/(sqrt(d)-1))*m/e.

    • Follows from: step 3 of alg. 1, at most 1/(e(i)-e(i-1)) items are sent by a node at height i to its parent

ICS280sensors, Winter 2005


Min total load algorithm2

Min Total-Load algorithm

  • Lemma: a tree in which each internal node of height I has at least d children of height i-1 is d-dominating

  • Construction of topology with large dominating factors:

    • Each node of height i+1, if has two or more children of heigh I, pins down any two of its children so that they can not switch parents, and flag itself.

    • Non-pinned nodes in each level j switch parents randomly to any other reachable non-flagged node in level j-1.

    • As soon as a non-flagged node has at least two flagged children of the same height, it pins both of them and the flags itself.

    • This makes the tree 2-dominating.

ICS280sensors, Winter 2005


Identify frequent items multi path algorithm

Identify frequent items–multi-path algorithm

  • Replace the + operator with duplicate-insensitive addition operators

  • Synopsis generation, fusion, and evaluation all depend on what duplicate-insensitive addition algorithm is used.

ICS280sensors, Winter 2005


Results

Results

ICS280sensors, Winter 2005


Results1

Results

ICS280sensors, Winter 2005


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