Journal of the ACM

Interference control and quality-of-service (QoS) awareness are the major challenges for resource management in orthogonal frequency-division multiple access femtocell networks This paper investigates a self-organization strategy for physical resource block (PRB) allocation with QoS constraints to avoid the co-channel and co-tiered interference Femtocell self-organization including self-configuration and self-optimization is proposed to manage the large femtocell networks We formulate the optimization problem for PRB assignments where multiple QoS classes for different services can be supported, and interference between femtocells can be completely avoided The proposed formulation pursues the maximization of PRB efficiency A greedy algorithm is developed to solve the resource allocation formulation In the simulations, the proposed approach is observed to increase the system throughput by over 13% without femtocell interference Simulations also demonstrate that the rejection ratios of all QoS classes are low and mostly below 10% Moreover, the proposed approach improves the PRB efficiency by over 82% in low-loading scenario and 13% in high-loading scenario

/pdf/resource-allocation-with-interference-avoidance-in-ofdma-19tiuhgzyc.pdf

Resource Allocation with Interference Avoidance in OFDMA Femtocell Networks

For a positive integer k, a k-coloring of a graph inline image is a mapping inline image such that inline image whenever inline image. The COLORING problem is to decide, for a given G and k, whether a k-coloring of G exists. If k is fixed (i.e., it is not part of the input), we have the decision problem k-COLORING instead. We survey known results on the computational complexity of COLORING and k-COLORING for graph classes that are characterized by one or two forbidden induced subgraphs. We also consider a number of variants: for example, where the problem is to extend a partial coloring, or where lists of permissible colors are given for each vertex.

/pdf/a-survey-on-the-computational-complexity-of-coloring-graphs-290lv8e457.pdf

A Survey on the Computational Complexity of Coloring Graphs with Forbidden Subgraphs

Background and Purpose— Recombinant tissue plasminogen activator (rtPA; Actilyse) is not as widely used in clinical practice as it could be. Have new data since 1995 strengthened the evidence sufficiently to justify more widespread use of rtPA? Methods— We performed a sequential year-to-year cumulative meta-analysis of randomized controlled trials of rtPA in acute ischemic stroke. Results— Although the amount of data has doubled since 1995, effect estimates for key outcomes remain imprecise, and significant between-trial heterogeneity persists. In the most recent analysis, rtPA up to 6 hours after stroke yielded 55 fewer dead or dependent people per 1000 treated (95% CI, 18 to 92) despite some risk (nonsignificant excess of 19 deaths per 1000 patients treated; 95% CI, 6 fewer to 48 more). Severity of stroke, patient age, and aspirin use were possible sources of heterogeneity. Conclusions— Despite doubling of the data since 1995, the magnitude of risks and benefits with rtPA remains imprecise. This gap in knowledge may be hindering clinical use of rtPA and can be filled only by new trials designed to address these specific issues.

Thrombolytic Therapy With Recombinant Tissue Plasminogen Activator for Acute Ischemic Stroke. Where Do We Go From Here? A Cumulative Meta-Analysis

For a positive integer $k$, a $k$-colouring of a graph $G=(V,E)$ is a mapping $c: V\rightarrow\{1,2,...,k\}$ such that $c(u)\neq c(v)$ whenever $uv\in E$. The Colouring problem is to decide, for a given $G$ and $k$, whether a $k$-colouring of $G$ exists. If $k$ is fixed (that is, it is not part of the input), we have the decision problem $k$-Colouring instead. We survey known results on the computational complexity of Colouring and $k$-Colouring for graph classes that are characterized by one or two forbidden induced subgraphs. We also consider a number of variants: for example, where the problem is to extend a partial colouring, or where lists of permissible colours are given for each vertex.

A Survey on the Computational Complexity of Colouring Graphs with Forbidden Subgraphs

Given a graph G = (V,E) and positive integral vertex weights w : V → N, the max-coloring problem seeks to find a proper vertex coloring of G whose color classes C1,C2,...,Ck, minimize Σki = 1maxν∈Ciw(ν). This problem, restricted to interval graphs, arises whenever there is a need to design dedicated memory managers that provide better performance than the general purpose memory management of the operating system. Specifically, companies have tried to solve this problem in the design of memory managers for wireless protocol stacks such as GPRS or 3G.Though this problem seems similar to the wellknown dynamic storage allocation problem, we point out fundamental differences. We make a connection between max-coloring and on-line graph coloring and use this to devise a simple 2-approximation algorithm for max-coloring on interval graphs. We also show that a simple first-fit strategy, that is a natural choice for this problem, yields a 10-approximation algorithm. We show this result by proving that the first-fit algorithm for on-line coloring an interval graph G uses no more than 10.x(G) colors, significantly improving the bound of 26.x(G) by Kierstead and Qin (Discrete Math., 144, 1995). We also show that the max-coloring problem is NP-hard.

Buffer minimization using max-coloring

https://doc.rero.ch/record/328806/files/triangle-free.pdf

Colouring vertices of triangle-free graphs without forests

Given a graph G = (V, E) and positive integral vertex weights w : V → N, the max-coloring problem seeks to find a proper vertex coloring of G whose color classes C1, C2, ..., Ck, minimize ${\sum_{i=1}^{k}}{\it max}_{v\epsilon C{_{i}} {\it w}(v)}$. The problem arises in scheduling conflicting jobs in batches and in minimizing buffer size in dedicated memory managers.

In this paper we present three approximation algorithms and one inapproximability result for the max-coloring problem. We show that if for a class of graphs ${\mathcal G}$, the classical problem of finding a proper vertex coloring with fewest colors has a c-approximation, then for that class ${\mathcal G}$ of graphs, max-coloring has a 4c-approximation algorithm. As a consequence, we obtain a 4-approximation algorithm to solve max-coloring on perfect graphs, and well-known subclasses such as chordal graphs, and permutation graphs. We also obtain constant-factor algorithms for max-coloring on classes of graphs such as circle graphs, circular arc graphs, and unit disk graphs, which are not perfect, but do have a constant-factor approximation for the usual coloring problem. As far as we know, these are the first constant-factor algorithms for all of these classes of graphs. For bipartite graphs we present an approximation algorithm and a matching inapproximability result. Our approximation algorithm returns a coloring whose weight is within $\frac{8}{7}$ times the optimal. We then show that for any e > 0, it is impossible to approximate max-coloring on bipartite graphs to within a factor of $(\frac{8}{7} - \epsilon)$ unless P = NP. Thus our approximation algorithm yields an optimum approximation factor. Finally, we also present an exact sub-exponential algorithm and a PTAS for max-coloring on trees.

/pdf/approximation-algorithms-for-the-max-coloring-problem-21swr3f7kc.pdf

Approximation algorithms for the max-coloring problem

Weighted geometric set-cover problems arise naturally in several geometric and nongeometric settings (e.g., the breakthrough of Bansal and Pruhs [Proceedings of FOCS, 2010, pp. 407--414] reduces a wide class of machine scheduling problems to weighted geometric set cover). More than two decades of research has succeeded in settling the $(1+\epsilon)$-approximability status for most geometric set-cover problems, except for some basic scenarios which are still lacking. One is that of weighted disks in the plane for which, after a series of papers, Varadarajan [Proceedings of STOC'10, 2010, pp. 641--648] presented a clever quasi-sampling technique, which together with improvements by Chan et al. [Proceedings of SODA, 2012, pp. 1576--1585], yielded an $O(1)$-approximation algorithm. Even for the unweighted case, a polynomial time approximation scheme (PTAS) for a fundamental class of objects called pseudodisks (which includes halfspaces, disks, unit-height rectangles, translates of convex sets, etc.) is curren...

Quasi-Polynomial Time Approximation Scheme for Weighted Geometric Set Cover on Pseudodisks and Halfspaces

Weighted geometric set-cover problems arise naturally in several geometric and non-geometric settings (e.g. the breakthrough of Bansal and Pruhs (FOCS 2010) reduces a wide class of machine scheduling problems to weighted geometric set-cover). More than two decades of research has succeeded in settling the (1+e)-approximability status for most geometric set-cover problems, except for four basic scenarios which are still lacking. One is that of weighted disks in the plane for which, after a series of papers, Varadarajan (STOC 2010) presented a clever quasi-sampling technique, which together with improvements by Chan et al(SODA 2012), yielded a O(1)-approximation algorithm. Even for the unweighted case, a PTAS for a fundamental class of objects called pseudodisks (which includes disks, unit-height rectangles, translates of convex sets etc.) is currently unknown. Another fundamental case is weighted halfspaces in R3, for which a PTAS is currently lacking. In this paper, we present a QPTAS for all of these remaining problems. Our results are based on the separator framework of Adamaszek and Wiese (FOCS 2013, SODA 2014), who recently obtained a QPTAS for weighted independent set of polygonal regions. This rules out the possibility that these problems are APX-hard, assuming NP DTIME(2polylog(n)). Together with the recent work of Chan-Grant (CGTA 2014), this settles the APX-hardness status for all natural geometric set-cover problems.

/pdf/settling-the-apx-hardness-status-for-geometric-set-cover-4ycr1w8weq.pdf

Rajiv Raman

Papers

Buffer minimization using max-coloring

Colouring vertices of triangle-free graphs without forests

Approximation algorithms for the max-coloring problem

Quasi-Polynomial Time Approximation Scheme for Weighted Geometric Set Cover on Pseudodisks and Halfspaces

Settling the APX-Hardness Status for Geometric Set Cover