16 research outputs found
On Ranges and Partitions in Optimal TCAMs
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. In the longest-prefix model (LPM), Draves et al.
(INFOCOM 1999) find a minimal representation of a function, and Sadeh et al.
(INFOCOM 2019) find a minimal representation of a partition. In certain
situations, range-functions are of special interest, that is, all the addresses
with the same target, or action, are consecutive. In this paper we show that
minimizing the amount of TCAM entries to represent a partition comes at the
cost of fragmentation, such that for some partitions some actions must have
multiple ranges. Then, we also study the case where each target must have a
single segment of addresses
Dynamic Binary Search Trees: Improved Lower Bounds for the Greedy-Future Algorithm
Binary search trees (BSTs) are one of the most basic and widely used data structures. The best static tree for serving a sequence of queries (searches) can be computed by dynamic programming. In contrast, when the BSTs are allowed to be dynamic (i.e. change by rotations between searches), we still do not know how to compute the optimal algorithm (OPT) for a given sequence. One of the candidate algorithms whose serving cost is suspected to be optimal up-to a (multiplicative) constant factor is known by the name Greedy Future (GF). In an equivalent geometric way of representing queries on BSTs, GF is in fact equivalent to another algorithm called Geometric Greedy (GG). Most of the results on GF are obtained using the geometric model and the study of GG. Despite this intensive recent fruitful research, the best lower bound we have on the competitive ratio of GF is 4/3. Furthermore, it has been conjectured that the additive gap between the cost of GF and OPT is only linear in the number of queries. In this paper we prove a lower bound of 2 on the competitive ratio of GF, and we prove that the additive gap between the cost of GF and OPT can be ?(m ? log log n) where n is the number of items in the tree and m is the number of queries
Caching Connections in Matchings
Motivated by the desire to utilize a limited number of configurable optical
switches by recent advances in Software Defined Networks (SDNs), we define an
online problem which we call the Caching in Matchings problem. This problem has
a natural combinatorial structure and therefore may find additional
applications in theory and practice.
In the Caching in Matchings problem our cache consists of matchings of
connections between servers that form a bipartite graph. To cache a connection
we insert it into one of the matchings possibly evicting at most two other
connections from this matching. This problem resembles the problem known as
Connection Caching, where we also cache connections but our only restriction is
that they form a graph with bounded degree . Our results show a somewhat
surprising qualitative separation between the problems: The competitive ratio
of any online algorithm for caching in matchings must depend on the size of the
graph.
Specifically, we give a deterministic competitive and randomized competitive algorithms for caching in matchings, where is the
number of servers and is the number of matchings. We also show that the
competitive ratio of any deterministic algorithm is
and of any randomized algorithm is . In particular, the lower bound for
randomized algorithms is regardless of , and can be as high
as if , for example. We also show that if we
allow the algorithm to use at least matchings compared to used by
the optimum then we match the competitive ratios of connection catching which
are independent of . Interestingly, we also show that even a single extra
matching for the algorithm allows to get substantially better bounds
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
The emergence of synaesthesia in a Neuronal Network Model via changes in perceptual sensitivity and plasticity
Synaesthesia is an unusual perceptual experience in which an inducer stimulus triggers a percept in a different domain in addition to its own. To explore the conditions under which synaesthesia evolves, we studied a neuronal network model that represents two recurrently connected neural systems. The interactions in the network evolve according to learning rules that optimize sensory sensitivity. We demonstrate several scenarios, such as sensory deprivation or heightened plasticity, under which synaesthesia can evolve even though the inputs to the two systems are statistically independent and the initial cross-talk interactions are zero. Sensory deprivation is the known causal mechanism for acquired synaesthesia and increased plasticity is implicated in developmental synaesthesia. The model unifies different causes of synaesthesia within a single theoretical framework and repositions synaesthesia not as some quirk of aberrant connectivity, but rather as a functional brain state that can emerge as a consequence of optimising sensory information processing
Optimal Weighted Load Balancing in TCAMs
Traffic splitting is a required functionality in networks, for example for
load balancing over multiple paths or among different servers. The capacities
of the servers determine the partition by 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. Previous work showed how to compute the smallest
prefix-matching TCAM necessary to implement a given partition exactly. In this
paper we solve the more practical case, where at most prefix-matching TCAM
rules are available, restricting the ability to implement exactly the desired
partition. We give simple and efficient algorithms to find rules that
generate a partition closest in to the desired one. We do the same
for a one-sided version of which equals to the maximum overload on a
server and for a relative version of it. We use our algorithms to evaluate how
the expected error changes as a function of the number of rules, the number of
servers, and the width of the TCAM.Comment: This is an extended version of a paper presented in ACM CoNEXT 202
A simple network architecture to study the conditions for evolution of cross-talk interactions.
<p>(A) The network contains four neurons, one input neuron and one output neuron in each modality. The feedforward connections are denoted by W<sub>11</sub> and W<sub>22</sub> and the recurrent cross-talk connections are denoted by K<sub>12</sub> (from neuron 2 to 1) and K<sub>21</sub> (from neuron 1 to 2). In this simple case, there are no internal recurrent connections within each modality, only between them. (B) The inputs were drawn from two independent Gaussian distributions with zero mean. We analysed the effect of the variances of the two Gaussian distributions on the evolution of cross-talk connections.</p
A network model for studying the evolution of synaesthetic mappings.
<p>A. Network architecture. The network is composed of two interacting modalities. Each modality receives a two-dimensional input characterized by an angle and a distance from the origin. This input is mapped into a high dimensional representation. There are recurrent connections among all the neurons in the output layer, namely within and between modalities. For clarity, only a few connections are shown. B. Feedforward connections and input distribution. The feedforward connections (red radial lines) are unit vectors with angles equally spaced from 0° to 360°. They are fixed throughout the learning. The input to each neuron is proportional to the projection of the input on the corresponding unit vector and has a cosine tuning around the corresponding angle, which represents its preferred feature. For clarity, the figure shows only a few lines, but in the numerical simulations we used 71 output neurons in each modality. The blue dots depict the input distribution to a single modality. The angles are uniformly distributed and the distance from the origin has a Gaussian distribution around a characteristic distance (0.1 in this example), which represents stimulus intensity.</p