40 research outputs found
Enumerating -arc-connected orientations
12 pagesWe study the problem of enumerating the -arc-connected orientations of a graph , i.e., generating each exactly once. A first algorithm using submodular flow optimization is easy to state, but intricate to implement. In a second approach we present a simple algorithm with delay and amortized time , which improves over the analysis of the submodular flow algorithm. As ingredients, we obtain enumeration algorithms for the -orientations of a graph in delay and for the outdegree sequences attained by -arc-connected orientations of in delay
Codes for Load Balancing in TCAMs: Size Analysis
Traffic splitting is a required functionality in networks, for example for
load balancing over paths or servers, or by the source's access restrictions.
The capacities of the servers (or the number of users with particular access
restrictions) determine the sizes of the parts into which traffic should be
split. A recent approach implements traffic splitting within the ternary
content addressable memory (TCAM), which is often available in switches. It is
important to reduce the amount of memory allocated for this task since TCAMs
are power consuming and are often also required for other tasks such as
classification and routing. Recent works suggested algorithms to compute a
smallest implementation of a given partition in the longest prefix match (LPM)
model. In this paper we analyze properties of such minimal representations and
prove lower and upper bounds on their size. The upper bounds hold for general
TCAMs, and we also prove an additional lower-bound for general TCAMs. We also
analyze the expected size of a representation, for uniformly random ordered
partitions. We show that the expected representation size of a random partition
is at least half the size for the worst-case partition, and is linear in the
number of parts and in the logarithm of the size of the address space
ON THE STRUCTURE AND INVARIANTS OF CUBICAL COMPLEXES
This dissertation introduces two new results for cubical complexes. The first is a simple statistic on noncrossing partitions that expresses each coordinate of the toric h-vector of a cubical complex, written in the basis of the Adin h-vector entries, as the total weight of all noncrossing partitions. This expression can then be used to obtain a simple combinatorial interpretation of the contribution of a cubical shelling component to the toric h-vector.
Secondly, a class of indecomposable permutations, bijectively equivalent to stan- dard double occurrence words, may be used to encode one representative from each equivalence class of the shellings of the boundary of the hypercube. Finally, an adja- cent transposition Gray code is constructed for this class of permutations, which can be implemented in constant amortized time
Multicoloured Random Graphs: Constructions and Symmetry
This is a research monograph on constructions of and group actions on
countable homogeneous graphs, concentrating particularly on the simple random
graph and its edge-coloured variants. We study various aspects of the graphs,
but the emphasis is on understanding those groups that are supported by these
graphs together with links with other structures such as lattices, topologies
and filters, rings and algebras, metric spaces, sets and models, Moufang loops
and monoids. The large amount of background material included serves as an
introduction to the theories that are used to produce the new results. The
large number of references should help in making this a resource for anyone
interested in beginning research in this or allied fields.Comment: Index added in v2. This is the first of 3 documents; the other 2 will
appear in physic
LIPIcs, Volume 248, ISAAC 2022, Complete Volume
LIPIcs, Volume 248, ISAAC 2022, Complete Volum
Optimal Algorithms for Ranked Enumeration of Answers to Full Conjunctive Queries
We study ranked enumeration of join-query results according to very general
orders defined by selective dioids. Our main contribution is a framework for
ranked enumeration over a class of dynamic programming problems that
generalizes seemingly different problems that had been studied in isolation. To
this end, we extend classic algorithms that find the k-shortest paths in a
weighted graph. For full conjunctive queries, including cyclic ones, our
approach is optimal in terms of the time to return the top result and the delay
between results. These optimality properties are derived for the widely used
notion of data complexity, which treats query size as a constant. By performing
a careful cost analysis, we are able to uncover a previously unknown tradeoff
between two incomparable enumeration approaches: one has lower complexity when
the number of returned results is small, the other when the number is very
large. We theoretically and empirically demonstrate the superiority of our
techniques over batch algorithms, which produce the full result and then sort
it. Our technique is not only faster for returning the first few results, but
on some inputs beats the batch algorithm even when all results are produced.Comment: 50 pages, 19 figure