Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userWake Up and Join Me! An Energy-Efficient Algorithm for Maximal Matching in Radio Networks
105
0
0.0
(
0
)
Added by
Thomas Hayes
Publication date
2021
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
We consider networks of small, autonomous devices that communicate with each other wirelessly. Minimizing energy usage is an important consideration in designing algorithms for such networks, as battery life is a crucial and limited resource. Working in a model where both sending and listening for messages deplete energy, we consider the problem of finding a maximal matching of the nodes in a radio network of arbitrary and unknown topology. We present a distributed randomized algorithm that produces, with high probability, a maximal matching. The maximum energy cost per node is $O(log^2 n)$, where $n$ is the size of the network. The total latency of our algorithm is $O(n log n)$ time steps. We observe that there exist families of network topologies for which both of these bounds are simultaneously optimal up to polylog factors, so any significant improvement will require additional assumptions about the network topology. We also consider the related problem of assigning, for each node in the network, a neighbor to back up its data in case of node failure. Here, a key goal is to minimize the maximum load, defined as the number of nodes assigned to a single node. We present a decentralized low-energy algorithm that finds a neighbor assignment whose maximum load is at most a polylog($n$) factor bigger that the optimum.
rate research
Read More
The study of approximate matching in the Massively Parallel Computations (MPC) model has recently seen a burst of breakthroughs. Despite this progress, however, we still have a far more limited understanding of maximal matching which is one of the central problems of parallel and distributed computing. All known MPC algorithms for maximal matching either take polylogarithmic time which is considered inefficient, or require a strictly super-linear space of $n^{1+Omega(1)}$ per machine. In this work, we close this gap by providing a novel analysis of an extremely simple algorithm a variant of which was conjectured to work by Czumaj et al. [STOC18]. The algorithm edge-samples the graph, randomly partitions the vertices, and finds a random greedy maximal matching within each partition. We show that this algorithm drastically reduces the vertex degrees. This, among some other results, leads to an $O(log log Delta)$ round algorithm for maximal matching with $O(n)$ space (or even mildly sublinear in $n$ using standard techniques). As an immediate corollary, we get a $2$ approximate minimum vertex cover in essentially the same rounds and space. This is the best possible approximation factor under standard assumptions, culminating a long line of research. It also leads to an improved $O(loglog Delta)$ round algorithm for $1 + varepsilon$ approximate matching. All these results can also be implemented in the congested clique model within the same number of rounds.
We design new serial and parallel approximation algorithms for computing a maximum weight $b$-matching in an edge-weighted graph with a submodular objective function. This problem is NP-hard; the new algorithms have approximation ratio $1/3$, and are relaxations of the Greedy algorithm that rely only on local information in the graph, making them parallelizable. We have designed and implemented Local Lazy Greedy algorithms for both serial and parallel computers. We have applied the approximate submodular $b$-matching algorithm to assign tasks to processors in the computation of Fock matrices in quantum chemistry on parallel computers. The assignment seeks to reduce the run time by balancing the computational load on the processors and bounding the number of messages that each processor sends. We show that the new assignment of tasks to processors provides a four fold speedup over the currently used assignment in the NWChemEx software on $8000$ processors on the Summit supercomputer at Oak Ridge National Lab.
We propose an extension of the join calculus with pattern matching on algebraic data types. Our initial motivation is twofold: to provide an intuitive semantics of the interaction between concurrency and pattern matching; to define a practical compilation scheme from extended join definitions into ordinary ones plus ML pattern matching. To assess the correctness of our compilation scheme, we develop a theory of the applied join calculus, a calculus with value passing and value matching. We implement this calculus as an extension of the current JoCaml system.
Maximal independent set (MIS), maximal matching (MM), and $(Delta+1)$-coloring in graphs of maximum degree $Delta$ are among the most prominent algorithmic graph theory problems. They are all solvable by a simple linear-time greedy algorithm and up until very recently this constituted the state-of-the-art. In SODA 2019, Assadi, Chen, and Khanna gave a randomized algorithm for $(Delta+1)$-coloring that runs in $widetilde{O}(nsqrt{n})$ time, which even for moderately dense graphs is sublinear in the input size. The work of Assadi et al. however contained a spoiler for MIS and MM: neither problems provably admits a sublinear-time algorithm in general graphs. In this work, we dig deeper into the possibility of achieving sublinear-time algorithms for MIS and MM. The neighborhood independence number of a graph $G$, denoted by $beta(G)$, is the size of the largest independent set in the neighborhood of any vertex. We identify $beta(G)$ as the ``right parameter to measure the runtime of MIS and MM algorithms: Although graphs of bounded neighborhood independence may be very dense (clique is one example), we prove that carefully chosen variants of greedy algorithms for MIS and MM run in $O(nbeta(G))$ and $O(nlog{n}cdotbeta(G))$ time respectively on any $n$-vertex graph $G$. We complement this positive result by observing that a simple extension of the lower bound of Assadi et.al. implies that $Omega(nbeta(G))$ time is also necessary for any algorithm to either problem for all values of $beta(G)$ from $1$ to $Theta(n)$. We note that our algorithm for MIS is deterministic while for MM we use randomization which we prove is unavoidable: any deterministic algorithm for MM requires $Omega(n^2)$ time even for $beta(G) = 2$.
We consider the problem of partial order production: arrange the elements of an unknown totally ordered set T into a target partially ordered set S, by comparing a minimum number of pairs in T. Special cases include sorting by comparisons, selection, multiple selection, and heap construction. We give an algorithm performing ITLB + o(ITLB) + O(n) comparisons in the worst case. Here, n denotes the size of the ground sets, and ITLB denotes a natural information-theoretic lower bound on the number of comparisons needed to produce the target partial order. Our approach is to replace the target partial order by a weak order (that is, a partial order with a layered structure) extending it, without increasing the information theoretic lower bound too much. We then solve the problem by applying an efficient multiple selection algorithm. The overall complexity of our algorithm is polynomial. This answers a question of Yao (SIAM J. Comput. 18, 1989). We base our analysis on the entropy of the target partial order, a quantity that can be efficiently computed and provides a good estimate of the information-theoretic lower bound.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
