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The partial gossip problem revisited

Konstantin Kokhas, Olga Bursian

Abstract

We present correct proof of G. Chung, Y.-J. Tsay result on partial gossip problem.

The partial gossip problem revisited

Abstract

We present correct proof of G. Chung, Y.-J. Tsay result on partial gossip problem.
Paper Structure (3 sections, 7 theorems, 14 equations, 9 figures)

This paper contains 3 sections, 7 theorems, 14 equations, 9 figures.

Table of Contents

  1. Lemmas
  2. Examples
  3. Proof of the theorem

Key Result

Theorem 1

1) $P(n,k)=\bigl\lceil\frac{2^{k-1}-1}{2^{k-1}}\cdot n\bigr\rceil$ for $n\geqslant 2^{k-1}-1=t_{-1}$. 2) If $t_i\leqslant n< t_{i-1}$, where $0\leqslant i\leqslant k-4$, then $P(n,k)= n+i$.

Figures (9)

  • Figure 1: In this example the communication graph is a minimal tree (solid lines, the thicker line the earlier call), that makes all persons $k$-informed (${k=4}$). Adding one preliminary call (dash line) makes the persons $(k+1)$-informed.
  • Figure 2: In these two exmples the communication graphs are trees (solid lines, the thicker line the earlier call), that makes all persons $k$-informed (${k=4}$). Adding two preliminary calls (dash lines) makes the persons $(k+2)$-informed.
  • Figure 3: First calls in $k$-informing tree
  • Figure 4: Case 3
  • Figure 5: Graph $G'$ (solid lies) and $i$ preliminary calls (dash lines), all persons are $k$-informed, $n=16$, $k=8$, $i=3$, $j=16$, $p=0$.
  • ...and 4 more figures

Theorems & Definitions (7)

  • Theorem 1
  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Lemma 4
  • Lemma 5
  • Lemma 6