Do you want to publish a course? Click here

Tight Bounds for the Min-Max Boundary Decomposition Cost of Weighted Graphs

88   0   0.0 ( 0 )
 Added by David Steurer
 Publication date 2006
and research's language is English
 Authors David Steurer




Ask ChatGPT about the research

Many load balancing problems that arise in scientific computing applications ask to partition a graph with weights on the vertices and costs on the edges into a given number of almost equally-weighted parts such that the maximum boundary cost over all parts is small. Here, this partitioning problem is considered for bounded-degree graphs G=(V,E) with edge costs c: E->R+ that have a p-separator theorem for some p>1, i.e., any (arbitrarily weighted) subgraph of G can be separated into two parts of roughly the same weight by removing a vertex set S such that the edges incident to S in the subgraph have total cost at most proportional to (SUM_e c^p_e)^(1/p), where the sum is over all edges e in the subgraph. We show for all positive integers k and weights w that the vertices of G can be partitioned into k parts such that the weight of each part differs from the average weight by less than MAX{w_v; v in V}, and the boundary edges of each part have cost at most proportional to (SUM_e c_e^p/k)^(1/p) + MAX_e c_e. The partition can be computed in time nearly proportional to the time for computing a separator S of G. Our upper bound on the boundary costs is shown to be tight up to a constant factor for infinitely many instances with a broad range of parameters. Previous results achieved this bound only if one has c=1, w=1, and one allows parts with weight exceeding the average by a constant fraction.



rate research

Read More

In this paper we present a new data structure for double ended priority queue, called min-max fine heap, which combines the techniques used in fine heap and traditional min-max heap. The standard operations on this proposed structure are also presented, and their analysis indicates that the new structure outperforms the traditional one.
We present a randomized algorithm that takes as input an undirected $n$-vertex graph $G$ with maximum degree $Delta$ and an integer $k > 3Delta$, and returns a random proper $k$-coloring of $G$. The distribution of the coloring is emph{perfectly} uniform over the set of all proper $k$-colorings; the expected running time of the algorithm is $mathrm{poly}(k,n)=widetilde{O}(nDelta^2cdot log(k))$. This improves upon a result of Huber~(STOC 1998) who obtained a polynomial time perfect sampling algorithm for $k>Delta^2+2Delta$. Prior to our work, no algorithm with expected running time $mathrm{poly}(k,n)$ was known to guarantee perfectly sampling with sub-quadratic number of colors in general. Our algorithm (like several other perfect sampling algorithms including Hubers) is based on the Coupling from the Past method. Inspired by the emph{bounding chain} approach, pioneered independently by Huber~(STOC 1998) and Haggstrom & Nelander~(Scand.{} J.{} Statist., 1999), we employ a novel bounding chain to derive our result for the graph coloring problem.
167 - Siu-Wing Cheng , Yuchen Mao 2018
The restricted max-min fair allocation problem seeks an allocation of resources to players that maximizes the minimum total value obtained by any player. It is NP-hard to approximate the problem to a ratio less than 2. Comparing the current best algorithm for estimating the optimal value with the current best for constructing an allocation, there is quite a gap between the ratios that can be achieved in polynomial time: roughly 4 for estimation and roughly $6 + 2sqrt{10}$ for construction. We propose an algorithm that constructs an allocation with value within a factor of $6 + delta$ from the optimum for any constant $delta > 0$. The running time is polynomial in the input size for any constant $delta$ chosen.
In a bipartite max-min LP, we are given a bipartite graph $myG = (V cup I cup K, E)$, where each agent $v in V$ is adjacent to exactly one constraint $i in I$ and exactly one objective $k in K$. Each agent $v$ controls a variable $x_v$. For each $i in I$ we have a nonnegative linear constraint on the variables of adjacent agents. For each $k in K$ we have a nonnegative linear objective function of the variables of adjacent agents. The task is to maximise the minimum of the objective functions. We study local algorithms where each agent $v$ must choose $x_v$ based on input within its constant-radius neighbourhood in $myG$. We show that for every $epsilon>0$ there exists a local algorithm achieving the approximation ratio ${Delta_I (1 - 1/Delta_K)} + epsilon$. We also show that this result is the best possible -- no local algorithm can achieve the approximation ratio ${Delta_I (1 - 1/Delta_K)}$. Here $Delta_I$ is the maximum degree of a vertex $i in I$, and $Delta_K$ is the maximum degree of a vertex $k in K$. As a methodological contribution, we introduce the technique of graph unfolding for the design of local approximation algorithms.
comments
Fetching comments Fetching comments
Sign in to be able to follow your search criteria
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا