Register Loading via Linear Programming

We study the following optimization problem. The input is a number k and a directed graph with a specified “start ” vertex, each of whose vertices may have one “memory bank requirement”, an integer. There are k “registers”, labeled 1...k. A valid solution associates to the vertices with no bank requirement one or more “load instructions ” L[b,j], for bank b and register j, such that every directed trail from the start vertex to some vertex with bank requirement c contains a vertex u that has been associated L[c,i] (for some register i ≤ k) and no vertex following u in the trail has been associated an L[b,i], for any other bank b. The objective is to minimize the total number of associated load instructions. We give a k(k +1)-approximation algorithm based on linear programming rounding, with (k+1) being the best possible unless Vertex Cover has approximation 2−ǫ for ǫ> 0. We also present a O(klogn) approximation, with n being the number of vertices in the input directed graph. Based on the same linear program, another rounding method outputs a valid solution with objective at most 2k times the optimum for k registers, using 2k−1 registers. This version of the paper corrects some minor errors that made it in the final Algorithmica paper.

An Improved Algorithm for Finding Maximum Outerplanar Subgraphs

We study the NP-complete Maximum Outerplanar Subgraph problem. The previous best known approximation ratio for this problem is 2/3. We propose a new approximation algorithm which improves the ratio to 7/10

An FPTAS of Minimizing Total Weighted Completion Time on Single Machine with Position Constraint

In this paper we study the classical scheduling problem of minimizing the total weighted completion time on a single machine with the constraint that one specific job must be scheduled at a specified position. We give dynamic programs with pseudo-polynomial running time, and a fully polynomial-time approximation scheme (FPTAS)

Approximation algorithms for graph-theoretic problems : planar subgraphs and multiway cut

Ph.D.Howard Karlof

Analytical Bounds on Broadcast with Hitch-hiking in Wireless Ad-HocNetworks

Abstract Recently, there have been papers indicating that the maximal ratio combiner device can result inenergy savings in wireless ad hoc networks by using Hitch-hiking. We study the Min-Energy Broadcast with Hitch-hiking problem, an idealized version of broadcast using hitch-hiking, a problem studied ex-perimentally in the INFOCOM 2004 paper of Agarwal et. al. Min-Energy Broadcast with Hitch-hiking captures the maximum savings one can achieve in broadcasting using maximal ratio combiners. Weshow that the optimum of the classical Min-Energy Broadcast problem is at most O(lo

Faster scaled matching

The rapidly growing need for analysis of digitized images in multimedia systems has lead to a variety of interesting problems in multidimensional pattern matching. One of the problems is that of scaled matching, finding all appearances of a pattern in a text in all discrete sizes. Another important problem is dictionary matching, quick search through a dictionary of preprocessed patterns in order to find all dictionary patterns that appear in the input text. In this paper we provide a very simple algorithm for two dimensional scaled matching. Our algorithm is first linear-time alphabet-independent scaled matching algorithm. Its running time is O (∣T∣), where ∣T∣ is the text size, and is independent of ∣∑∣, the size of the alphabet. Our technique generalizes to produce he first known algorithm for scaled dictionary matching. We can find all appearances of all dictionary patterns that appear in the input text in any discrete scale. The time bounds of our algorithm are equal to the best known exact (no scaling) two dimensional dictionary matching algorithms