Some improved bounds on communication complexity via new decomposition of cliques
نویسنده
چکیده
An ordered biclique partition of the complete graph Kn on n vertices is a collection of bicliques (i.e., complete bipartite graphs) such that (i) every edge of Kn is covered by at least one and at most two bicliques in the collection, and (ii) if an edge e is covered by two bicliques then each endpoint of e is in the first class in one of these bicliques and in the second class in other one. We show in this note that the minimum size of such a collection is O(n). This gives new results on two problems related to communication complexity. Namely, (i) a new separation between the size of a fooling set and the rank of a 0/1-matrix, and (ii) an improved lower bound on the nondeterministic communication complexity of the clique vs. independent set problem are given. keywords communication complexity, complete graphs, biclique partition, fooling set, rank
منابع مشابه
Improved Lower Bounds for Sum Coloring via Clique Decomposition
Given an undirected graph G = (V,E) with a set V of vertices and a set E of edges, the minimum sum coloring problem (MSCP) is to find a legal vertex coloring of G, using colors represented by natural numbers 1, 2, ... such that the total sum of the colors assigned to the vertices is minimized. This paper describes an approach based on the decomposition of the original graph into disjoint clique...
متن کاملLower Bounds for Approximating Graph Parameters via Communication Complexity
In a celebrated work, Blais, Brody, and Matulef [5] developed a technique for proving property testing lower bounds via reductions from communication complexity. Their work focused on testing properties of functions, and yielded new lower bounds as well as simplified analyses of known lower bounds. Here, we take a further step in generalizing the methodology of [5] to analyze the query complexi...
متن کاملSome new bounds on the general sum--connectivity index
Let $G=(V,E)$ be a simple connectedgraph with $n$ vertices, $m$ edges and sequence of vertex degrees$d_1 ge d_2 ge cdots ge d_n>0$, $d_i=d(v_i)$, where $v_iin V$. With $isim j$ we denote adjacency ofvertices $v_i$ and $v_j$. The generalsum--connectivity index of graph is defined as $chi_{alpha}(G)=sum_{isim j}(d_i+d_j)^{alpha}$, where $alpha$ is an arbitrary real<b...
متن کاملLower bounds on the signed (total) $k$-domination number
Let $G$ be a graph with vertex set $V(G)$. For any integer $kge 1$, a signed (total) $k$-dominating functionis a function $f: V(G) rightarrow { -1, 1}$ satisfying $sum_{xin N[v]}f(x)ge k$ ($sum_{xin N(v)}f(x)ge k$)for every $vin V(G)$, where $N(v)$ is the neighborhood of $v$ and $N[v]=N(v)cup{v}$. The minimum of the values$sum_{vin V(G)}f(v)$, taken over all signed (total) $k$-dominating functi...
متن کاملComparison of Clique-Listing Algorithms
This paper compares several published algorithms which list all of the maximal cliques of a graph. A clique is a complete subgraph, i.e., a set of vertices and edges such that every pair of vertices is joined by an edge. A maximal clique is a clique which is not a proper subgraph of a larger clique. A closely related concept is that of a maximal independent set (MIS), where every pair of vertic...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Discrete Applied Mathematics
دوره 166 شماره
صفحات -
تاریخ انتشار 2014