Cyclic quorum
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The document discusses cyclic quorums, which are a type of quorum design where groups (quorums) are assigned to people such that certain intersection and membership properties are satisfied with minimal size k. A cyclic quorum imposes the additional restriction that the quorums have a cyclic property where members of each quorum are spaced cyclically. The document provides an example of an optimal cyclic quorum design and discusses techniques for performing exhaustive searches to find optimal cyclic quorum designs such as pruning and isomorphic rejection.
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![Introduction
• Originally proposed by [Luk and Wong 97]
• Now utilized in different areas:
– Power-saving protocols/wakeup scheduling
– Control channel establishment in cognitive radio
network
– Anti-jamming communication
– Suffix array construction](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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○ 개요
현재 많은 연구자들이 network를 깊고 넓게 설계함으로써 높은 인식률을 갖는 네트워크를 얻고 있다. Network의 크기가 증가하면서 parameter와 computation의 수가 증가하게 되었고, 이러한 문제를 해결하기 위하여 pruning을 기반으로 한 압축 알고리즘들이 제안되어 왔다. 하지만 이러한 방법을 이용하여서는 network architecture자체를 바꿀 수 없기 때문에, 구조에서 오는 한계점들은 해결할 수 없었다.
Network recasting은 구조의 특성으로 인하여 발생하는 한계들을 해결하기 위하여 network architecture 자체를 바꾸는 방법이다. Network recasting을 이용하면 network를 구성하고있는 block들을 다른 형태의 block으로 변환을 할 수 있게 된다. Block-wise recasting 방법을 사용하여 각 block들을 변환할 수 있고, 해당 방법을 연속하여 적용함으로써 전체 network의 구조를 바꿀 수 있다. Sequential recasting 방법을 이용하게 되면 inference accuracy를 더욱 잘 보존할 수 있고, 또한 network architecture에 상관 없이 vanishing gradient problem을 완화 시킬 수 있다. Network recasting을 같은 network architecture에 적용하게 되면 parameter와 computation을 줄이는 효과를 얻을 수 있고, 다른 종류의 network architecture로 변환하게 되면 network를 가속시킬 수 있다. 이러한 경우에는 network architecture 자체를 변경할 수 있기 때문에 구조적 한계보다 더 높은 속도 향상을 얻을 수 있다.
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Cyclic quorum
- 1. Cyclic Quorum Wai-Shing Luk luk@fudan.edu.cn
- 2. Introduction • Originally proposed by [Luk and Wong 97] • Now utilized in different areas: – Power-saving protocols/wakeup scheduling – Control channel establishment in cognitive radio network – Anti-jamming communication – Suffix array construction
- 3. Quorum Design Problem • N people are assigned to k groups (quorum) such that: 1. For each pair of quorums, there is at least one person who is a member of both groups (Non- empty intersection property) 2. Each quorum contain exactly k people 3. Each person joins exactly k quorums • Question: – How the groups are designed with minimal k?
- 4. Example: N=8, k=4 • B0 = { 0, 1, 2, 4 } • B1 = { 1, 2, 3, 5 } • B2 = { 2, 3, 4, 6 } <-- • B3 = { 3, 4, 5, 7 } • B4 = { 4, 5, 6, 0 } • B5 = { 5, 6, 7, 1 } <-- • B6 = { 6, 7, 0, 2 } • B7 = { 7, 0, 1, 3 }
- 5. Some Facts • For a fixed k, the maximal value of N is k(k-1) + 1. Hence, the theoretical lower bound of k for a given N is ~sqrt(N). • If N = k(k-1)+1 and n=k-1 is prime power, the solution can be constructed via a finite projective plane of order n. • In general, optimal solution is very hard to find.
- 6. Cyclic Quorum • Impose one more restriction: a set of quorums has a cyclic property. • In the previous example, Bi = { 0+i, 1+i, 2+i, 4+i } modulo 8. • Advantage: the whole solution can be specified by just one single quorum. Hence, easy to hard coded in hardware. • Exhaustive search method is used for finding the optimal solution.
- 7. Techniques for Exhaustive Search • Pruning: – Detect partial solutions which cannot generate optimal solution. • Isomorphic rejection: – E.g. Let B1 = {a0, a1, …, an}. We can always assume that a0 = 1 and a1 = 2. – Also we can search only with ak floor(N/2)
- 8. Table of Optimal Cyclic Quorums