Connections between two cycles — a new design of dense processor interconnection networks

AbstractIn this paper we attempt to maximize the order of graphs of given degree Δ and diameter D. These graphs, which are known as (Δ, D) graphs, are used as dense interconnection networks, i.e., processors with relatively few links are connected with relatively short paths. The method described in this paper uses periodic connections between two cycles of the same length. The results obtained give a significant improvement of the known lower bounds in many cases. Large bipartite graphs with a given degree and diameter were also obtained by our method. Again, the improvement of the lower bounds is significant

Distributed Approximation of Maximum Independent Set and Maximum Matching

We present a simple distributed $\Delta$-approximation algorithm for maximum weight independent set (MaxIS) in the $\mathsf{CONGEST}$ model which completes in $O(\texttt{MIS}(G)\cdot \log W)$ rounds, where $\Delta$ is the maximum degree, $\texttt{MIS}(G)$ is the number of rounds needed to compute a maximal independent set (MIS) on $G$, and $W$ is the maximum weight of a node. %Whether our algorithm is randomized or deterministic depends on the \texttt{MIS} algorithm used as a black-box. Plugging in the best known algorithm for MIS gives a randomized solution in $O(\log n \log W)$ rounds, where $n$ is the number of nodes. We also present a deterministic $O(\Delta +\log^* n)$-round algorithm based on coloring. We then show how to use our MaxIS approximation algorithms to compute a $2$-approximation for maximum weight matching without incurring any additional round penalty in the $\mathsf{CONGEST}$ model. We use a known reduction for simulating algorithms on the line graph while incurring congestion, but we show our algorithm is part of a broad family of \emph{local aggregation algorithms} for which we describe a mechanism that allows the simulation to run in the $\mathsf{CONGEST}$ model without an additional overhead. Next, we show that for maximum weight matching, relaxing the approximation factor to ($2+\varepsilon$) allows us to devise a distributed algorithm requiring $O(\frac{\log \Delta}{\log\log\Delta})$ rounds for any constant $\varepsilon>0$. For the unweighted case, we can even obtain a $(1+\varepsilon)$-approximation in this number of rounds. These algorithms are the first to achieve the provably optimal round complexity with respect to dependency on $\Delta$

Distributed Approximation on Power Graphs

We investigate graph problems in the following setting: we are given a graph $G$ and we are required to solve a problem on $G^2$. While we focus mostly on exploring this theme in the distributed CONGEST model, we show new results and surprising connections to the centralized model of computation. In the CONGEST model, it is natural to expect that problems on $G^2$ would be quite difficult to solve efficiently on $G$, due to congestion. However, we show that the picture is both more complicated and more interesting. Specifically, we encounter two phenomena acting in opposing directions: (i) slowdown due to congestion and (ii) speedup due to structural properties of $G^2$. We demonstrate these two phenomena via two fundamental graph problems, namely, Minimum Vertex Cover (MVC) and Minimum Dominating Set (MDS). Among our many contributions, the highlights are the following. - In the CONGEST model, we show an $O(n/\epsilon)$-round $(1+\epsilon)$-approximation algorithm for MVC on $G^2$, while no $o(n^2)$-round algorithm is known for any better-than-2 approximation for MVC on $G$. - We show a centralized polynomial time $5/3$-approximation algorithm for MVC on $G^2$, whereas a better-than-2 approximation is UGC-hard for $G$. - In contrast, for MDS, in the CONGEST model, we show an $\tilde{\Omega}(n^2)$ lower bound for a constant approximation factor for MDS on $G^2$, whereas an $\Omega(n^2)$ lower bound for MDS on $G$ is known only for exact computation. In addition to these highlighted results, we prove a number of other results in the distributed CONGEST model including an $\tilde{\Omega}(n^2)$ lower bound for computing an exact solution to MVC on $G^2$, a conditional hardness result for obtaining a $(1+\epsilon)$-approximation to MVC on $G^2$, and an $O(\log \Delta)$-approximation to the MDS problem on $G^2$ in \mbox{poly}\log n rounds.Comment: Appears in PODC 2020. 40 pages, 7 figure

Methotrexate enhances the anti-inflammatory effect of CF101 via up-regulation of the A(3 )adenosine receptor expression

Methotrexate (MTX) exerts an anti-inflammatory effect via its metabolite adenosine, which activates adenosine receptors. The A(3 )adenosine receptor (A(3)AR) was found to be highly expressed in inflammatory tissues and peripheral blood mononuclear cells (PBMCs) of rats with adjuvant-induced arthritis (AIA). CF101 (IB-MECA), an A(3)AR agonist, was previously found to inhibit the clinical and pathological manifestations of AIA. The aim of the present study was to examine the effect of MTX on A(3)AR expression level and the efficacy of combined treatment with CF101 and MTX in AIA rats. AIA rats were treated with MTX, CF101, or both agents combined. A(3)AR mRNA, protein expression and exhibition were tested in paw and PBMC extracts from AIA rats utilizing immunohistochemistry staining, RT-PCR and Western blot analysis. A(3)AR level was tested in PBMC extracts from patients chronically treated with MTX and healthy individuals. The effect of CF101, MTX and combined treatment on A(3)AR expression level was also tested in PHA-stimulated PBMCs from healthy individuals and from MTX-treated patients with rheumatoid arthritis (RA). Combined treatment with CF101 and MTX resulted in an additive anti-inflammatory effect in AIA rats. MTX induced A(2A)AR and A(3)AR over-expression in paw cells from treated animals. Moreover, increased A(3)AR expression level was detected in PBMCs from MTX-treated RA patients compared with cells from healthy individuals. MTX also increased the protein expression level of PHA-stimulated PBMCs from healthy individuals. The increase in A(3)AR level was counteracted in vitro by adenosine deaminase and mimicked in vivo by dipyridamole, demonstrating that receptor over-expression was mediated by adenosine. In conclusion, the data presented here indicate that MTX induces increased A(3)AR expression and exhibition, thereby potentiating the inhibitory effect of CF101 and supporting combined use of these drugs to treat RA

Methotrexate enhances the anti-inflammatory effect of CF101 via up-regulation of the A(3 )adenosine receptor expression

Methotrexate (MTX) exerts an anti-inflammatory effect via its metabolite adenosine, which activates adenosine receptors. The A(3 )adenosine receptor (A(3)AR) was found to be highly expressed in inflammatory tissues and peripheral blood mononuclear cells (PBMCs) of rats with adjuvant-induced arthritis (AIA). CF101 (IB-MECA), an A(3)AR agonist, was previously found to inhibit the clinical and pathological manifestations of AIA. The aim of the present study was to examine the effect of MTX on A(3)AR expression level and the efficacy of combined treatment with CF101 and MTX in AIA rats. AIA rats were treated with MTX, CF101, or both agents combined. A(3)AR mRNA, protein expression and exhibition were tested in paw and PBMC extracts from AIA rats utilizing immunohistochemistry staining, RT-PCR and Western blot analysis. A(3)AR level was tested in PBMC extracts from patients chronically treated with MTX and healthy individuals. The effect of CF101, MTX and combined treatment on A(3)AR expression level was also tested in PHA-stimulated PBMCs from healthy individuals and from MTX-treated patients with rheumatoid arthritis (RA). Combined treatment with CF101 and MTX resulted in an additive anti-inflammatory effect in AIA rats. MTX induced A(2A)AR and A(3)AR over-expression in paw cells from treated animals. Moreover, increased A(3)AR expression level was detected in PBMCs from MTX-treated RA patients compared with cells from healthy individuals. MTX also increased the protein expression level of PHA-stimulated PBMCs from healthy individuals. The increase in A(3)AR level was counteracted in vitro by adenosine deaminase and mimicked in vivo by dipyridamole, demonstrating that receptor over-expression was mediated by adenosine. In conclusion, the data presented here indicate that MTX induces increased A(3)AR expression and exhibition, thereby potentiating the inhibitory effect of CF101 and supporting combined use of these drugs to treat RA