Filed under: Uncategorized | Tags: distributed computing, interactive computation, reliability, theory

How do you compute over a noisy channel? Say Alice and Bob want to run a distributed algorithm, but they can only communicate over a channel where each bit is flipped either stochastically or adversarially. What is the smallest number of bits they must send in order to obtain the correct output of the algorithm, with high probability? This general problem is called Interactive Communication, or sometimes Interactive Coding/Computation – let’s use IC for short. It doesn’t take much imagination to think of applications of IC: enabling sensor nodes to compute a function on their inputs in a noisy environment; designing reliable algorithms for natural algorithms [1]; and designing attack-resistant algorithms [2], just as some examples.

Wait, you may be thinking, isn’t this problem solved by error correcting codes? No – the bits sent in the distributed algorithm may be determined only one at a time, in a dynamic manner. Even for stochastic noise, if we naively encode each bit sent, in order to get a union bound ensuring the probability of any decoding error is small, we’ll need logarithmic blowup for each bit. We can do better.

In fact, in the first paper on this problem, Coding for Interactive Communication, Leonard Schulman described an algorithm that requires only constant blowup, even when a constant fraction of the bits on the channel are flipped **adversarially**. Schulman’s algorithm was based on a new type of code, tree codes, designed specifically for interactive communication. After this paper was published in 1996, subsequent work focused on improving the error tolerance of Schulman’s algorithm (i.e. tolerating a larger constant fraction of errors); tuning the communication blowup to the (known) error rate; and considering the situation where the computation occurs over more than 2 parties. See the survey paper Coding for interactive computation: progress and challenges (especially Sections 3 and 4) for details.

I’ll note here that in a sense all of information theory can be though of as a subset of IC. In particular, information theory considers “only” the class of distributed algorithms where Alice has an input that she wants to send to Bob. In IC, we need to handle all possible distributed algorithms, and so in a way, it’s pretty amazing that a constant adversarial noise rate can even be tolerated.

A very recent breakthrough in IC occurred in FOCS 2014, where Bernhard Haeupler in the paper Interactive Channel Capacity Revisited, made huge progress on the problem of tuning the communication blowup to a known error rate. In particular, he described an algorithm that given a fixed and known adversarial noise rate \epsilon, achieves a communication blowup as a function of \epsilon that is conjectured to be optimal.

So what if \epsilon is not known in advance? I’m going to end this post with a short advertisement for a recent paper with some collaborators of mine that begins to address that problem. The paper is Interactive Communication with Unknown Noise Rate, with Varsha Dani, Mahnush Movahedi, and Maxwell Young that will be in this upcoming ICALP. This is the first paper I’ve written about IC, and I hope it won’t be the last. In fact, I’d like to see more people in the distributed computing community consider the problem. In particular, it’d be nice to make progress on the (currently very hard) problem of somehow generalizing results to more than 2 parties.

[1] For example, see this paper for a closely related problem: Breathe before Speaking: Efficient Information Dissemination Despite Noisy, Limited and Anonymous Communication

[2] This last domain is particularly interesting to me. An obvious connection is attacks on communication channels. A less-obvious connection is attacks on nodes. If communication from each node is bounded, as is increasingly common for algorithms on large networks, there may be a fairly tight connection between attacks on communication channels and attacks on nodes. Thus, there may be connections to attacks like Byzantine faults.

If you’re in New Haven next week, you could do worse than checking out this talk at Yale’s CS Colloquium by my stellar PhD student Mahdi Zamani.

Congratulations to Dr. George Saad who just defended his dissertation (with distinction) yesterday on “Selfishness and Malice in Distributed Systems”. George’s dissertation focused on designing 1) algorithms for self-healing in networks with Byzantine nodes and 2) designing mediators to improve social welfare in a type of El-Farol game with both positive and negative networks effects. Here are slides from his excellent talk.

George will be taking a position at the Silicon Valley startup Jasper Technologies next month. On his committee were Maxwell Young (Drexel University), Tom Hayes and Dorian Arnold.

Congratulations George!

Filed under: Uncategorized | Tags: Byzantine agreement, spectral analysis, theory

I gave a talk last week at SOFSEM 2015. The talk covers some of our recent work that uses spectral analysis to solve a classic Byzantine agreement problem. Here are the slides.

Congratulations to the 2014 ACM Fellows, especially my friend and frequent collaborator Valerie King. As usual, there are many theoreticians including Allan Borodin, Faith Ellen, Michael Mitzenmacher, Aravind Srinivisan. The (somewhat) surprising thing is that *all* of these theoreticians have done significant work in distributed algorithms or networks.

Filed under: Uncategorized | Tags: distributed computing, natural algorithms, theory

*[The following report on BDA’14 was written by my student Mahdi Zamani]*

*[A more polished version of this report is available HERE]*

*Biological Distributed Algorithms*co-located with DISC 2014. The workshop consisted of 20 talks distributed in two days and focused on the relationships between distributed computing and distributed biological systems and in particular, on analysis and case studies that combine the two. The following is a summary of some of the talks we found interesting.

### Insect Colonies and Distributed Algorithms; Insect Colony Researcher Viewpoint**, **Anna Dornhaus,* University of Arizona*

Anna talked about several open questions in modeling the behavior of different insect colonies. Insect colonies go through many changes over time in response to their changing needs and environment.

Most changes happen via complex collective behaviors such as task allocation, foraging (food finding), nest building, load transport, etc. One interesting aspect of insect colonies is that unreliable individual behaviors result in complex group behaviors that are reliable. Individuals use various methods of communication such as pheromone trails, versatile signals, visual cues, substrate vibration, and waggle dance. Waggle dance is a sophisticated method of communication among honeybees to indicate resource locations by showing the angle from sun. Biologists are generally interested in computer models to know how individual behaviors impact group behaviors. In particular, they are interested to understand how *positive feedbacks* (a process A produces more of another process B which in turn produces more of A and so on) lead to significant consequences such as symmetry breaking. For example, ants tend to choose from one food source even if there are multiple similar sources around them. Also, larger colonies result in more symmetry breaking behavior. This motivates the following questions: How does the size of a colony affect collective behavior? Why is the workload distribution so uneven in some biological systems?

### Distributed Algorithms and Biological Systems**, **Nancy Lynch,* MIT*

*simple*states that follow

*simple*rules. To model a bio system using a distributed algorithm, the first step is to define the problem, the platform (physical capabilities of the system such as memory), and the strategies (rules).

*leader election*and

*maximal independent sets (MIS)*. In leader election, there is a ring of processes that can communicate with their neighbors and the goal is to pick a leader process. If the processes are all identical and their behaviors are deterministic, then solving this problem is impossible due to symmetry (all processes are similar). On the other hand, if the processes are not identical (

*i.e.*, each has a unique ID), then finding a leader is possible. Interestingly, in a setting with identical processes that are allowed to make random choices, this problem can be solved using a biased coin: each party flips a coin with probability 1/n to announce itself as the leader.

*i.e.*, vertices connected directly via an edge) are both in the subset. There is a Las Vegas algorithm [B] for solving this problem: in each of several rounds, each party flips a biased coin and informs its neighbors that it is in the MIS if it has not received a similar message from its neighbors. Each party stops if either it is in MIS or one of its neighbors in the MIS. Nancy finally talked about three ant colony problems that her research group has recently been working on: Ants foraging, house hunting, and task allocation.

### Modeling Slime Mold Networks**, **Saket Navlakha,* CMU*

Saket then continued by describing their model of the slime mold behavior for finding food sources. For simplicity, they assume there is a complete graph at first and then by calculating flow over the edges (tubes) some of the edges are disconnected. Then, they measured and compared the cost, efficiency, and fault tolerance of the network generated by their model and the Tokyo rail system: their model is as efficient as the rail system! The brain development has a similar behavior: it generates a complete neural network at first and then prunes over time. This is called the *synaptic pruning algorithm*.

The human brain starts with a very dense network of neurons and each edge keeps track of the number of times it is used to route information based on some pre-determined distribution. Then, the network is pruned based on the flow information. Saket finally talked about a similar distributed model for bacterial foraging (E. coli) in complicated terrains.

### Collective Load Transport in Ants**, **Ofer Feinerman,* Weizmann Institute*

*collective load retrieval*, the process in which a large number of ants cooperate to carry a large food item to the nest. Ofer’s research team tracked a group of ants and the load over distances of about 1000 ant lengths and used image analysis to obtain highly detailed information. They showed that the collective motion is highly cooperative and guided by temporary leaders that are knowledgeable regarding the correct direction home. Ofer finally presented a theoretical model suggesting that the ant-load system is poised at a critical point between random and ballistic motions which renders it highly susceptible to a knowledgeable leader. He played a video showing a group of ants carrying their load in a wrong direction. Then, one ant joined the group as the leader and corrected the direction.

### Distributed Information Processing by Insect Societies**, **Stephen Pratt,* Arizona State University*

Stephen talked about a collective model of optimal house-hunting in rock ant *Temnothorax albipennis.* Each colony of T. albipennis has a single queen and hundreds of scouts (workers). In the process of house-hunting, scouts first discover new nests and assess them according to some criteria such as size and darkness. Then, they recruit other ants to the new nest using *tandem running*, where an informed ant leads a second ant to her destination to get a second opinion about the nest (see Figure 3↓).

When the number of ants in the new nest reaches a threshold, scouts begin rapid *transport* of the rest of the colony by carrying nest-mates. In each time step, each ant is in one of these three states: *explore*, *tandem*, and *transport*. The transition between these states happens based on the ant’s evaluation of the quality of the nest sites and the population of the ants in this sites. Stephen defines optimality with regards to the speed and accuracy of the decision-making process. He asked: Does a colony have a greater cognitive capacity than an individual? For the house-hunting process, recent lab experiments show that when the number of nests (choices) increases, colony performs much better in choosing the good choices while lone ants visit more nests. He then asked: Do colonies make more precise discriminations than individuals? To answer this, Stephen’s team ran experiments to measure how individuals and colonies can correctly compare a dark nest with nests with various brightness levels. Interestingly, they observed that colonies can correctly choose darker nests with significantly more accuracy than individuals. They also show that even two ants perform significantly better than one.

### Cells, Termites, and Robot Collectives**, **Radhika Nagpal,* Harvard University*

Radhika talked about biological systems from an engineering viewpoint. Collective behaviors often result in self-repairing and self-organizing properties which are crucial for building robust systems. In bio systems, these properties are achieved from cooperation of vast numbers of unreliable agents.

Radhika described a bio-inspired distributed robot system that can perform group tasks such as collective construction, collective transport, and pattern/shape formation. The robots achieve a desired global goal in a completely decentralized fashion by performing local interactions with other robots. In particular, they model a large population of termites for building complex structures (see Figure 4↑).

### Confidence Sharing: An Economic Strategy for Efficient Information Flows in Animal Groups**, **Amos Korman,* CNRS and University of Paris Diderot*

*passive (indirect)*and

*active (direct)*communication. Passive communication is done by transferring information with no direct intention of signaling,

*i.e.*, cues from the behavior of one animal are indirectly perceived by others. For example, it is shown that animals align their movements to those performed by their neighbors. In active communication, an animal communicates directly with others by sending parts of its internal state via, for example, pheromone trails, cell signaling, etc. Amos then continued his talk by arguing that confidence exists among animals: they are shown to become more responsive as their certainty drops. For example, crickets increase their speed when they are more confident about their intention. This confidency is propagated from one cricket to others via passive and active communication. By sharing their confidence, agents improve their unreliable individual estimates. Amos described an algorithm in which each agent compresses all information it has gathered into a single parameter that represents its confidence in its behavior. This gives a very simple and near optimal algorithm. The algorithm continuously updates agents confidence level based on the interaction it has with other agents. Unfortunately, if there are bandwidth and computational restrictions to agents, then the performance of this algorithm decreases significantly. Also, the algorithm assumes two agents who exchange confidence information must have disjoint set of exchange history.

### Task Allocation in Ant Colonies**, **Alex Cornejo,* Harvard University*

*[The following blog report on SSS’14 was written by my student **George Saad**]*

*16th **International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS 2014)* was held in Paderborn, Germany, from Sep 28 to Oct 1, 2014. This conference discusses the design and development of distributed systems with fault-tolerance and self-* properties.

SSS 2014 had seven sessions: self-stabilization I/II/III; Dependable Systems; Formal Methods, Safety, and Security; Ad-hoc, Sensor and Mobile Networks and Cyberphysical Systems; and Cloud Computing, P2P, Self-organizing and Autonomous Systems.

On the first day, which was tutorial day on Self-Organizing Physical Systems, *Marco Dorigo*, a professor in Universite Libre de Bruxelles and University of Paderborn, gave the fourth talk for Self-organizing Swarms. In this talk, Dorigo showed how to use ants to find the shortest path of a pair of nodes in a network using artificial pheromones. The ants choose one path from a set of paths stochastically, depending on the amount of pheromones of previous ants visited such paths. Note that there are other strategies considered for solving this problem such as separation, alignment and cohesion. Interestingly, finding the shortest path in this way can be used to obtain arg min f(x).

However, artificial pheromones are not practical in many situations. Thus, goal search and path formation are studied in the absence of pheromones. In particular, robots are assigned as points in order to form a path to the goal, after which all other robots will follow such path.

Homogenous robots can cooperate together to perform tasks that cannot be done by individual robots, such as crossing big holes and climbing steep hills. Adaptive rotation is one of the strategies to enable a group of robots to climb high hills. Moreover, the robots do light-flashing to synchronize in order to cooperate properly.

Heterogeneous robots are also considered. Note that they are heterogeneous in the sense that they have different capabilities. Thus, they work together to empower their combined capabilities in order to perform harder tasks. For instance, there are three types of robots: eye-robot, arm-robot and foot-robot. In a popular scenario, they cooperate together to look for and bring a book. First, a eye-robot flies seeking for the book. Once the book is located. A set of foot-robots is notified in order to move to that location carrying an arm-robot. Eventually, the arm-robot catches the book. After that, all these robots return back to the starting point.

In Self-Stabilization I session, *Volker Turau*, a professor in Hamburg University of Technology, presented his paper, “A self-stabilizing algorithm for edge monitoring problem”.

In wireless sensor networks, the nodes sense the environment and transmit (or forward) the data in the network. In the presence of adversary, a set of compromised nodes may disrupt the network in the sense of corrupting or dropping messages. Thus, a set of nodes is chosen in order to monitor all communications on edges using k-hop knowledge. In k-hop knowledge, a monitoring node x can monitor the communication on any edge whose endpoint is reachable by at most k hops from node x. The challenging task is to find the minimum set of monitoring nodes in a network. This problem is NP-Complete even for 1-hop knowledge.

Two distributed approximation algorithms are provided as previous work to solve this problem in synchronous model with no transient faults. In this paper, the authors provided a self-stabilizing algorithm, which finds the minimum set of monitoring nodes in the presence of transient faults in asynchronous model. In this algorithm, each node has a state which determines if this node is in or out of the monitoring set, and each node maintains a set of monitoring nodes for each of its adjacent edges. In each step of the algorithm, the state of each node changes only after having the permission of all neighboring nodes.

We presented our paper, *Self-Healing Computation*, in Self-Stabilization II session. Our contribution is that we developed a self-healing algorithm, for computation networks, which 1) detects computation corruptions made by Byzantine nodes; and 2) segregates such nodes, so that eventually no more corruptions occur.

We show that our self-healing algorithm reduces asymptotically the message cost compared to non-self-healing algorithms. Moreover, our experimental results show that the message cost is reduced by a factor of 425 compared to the naïve computation for a network of size 8k.

In this paper, we have an interesting result: informally, given any tree of size n, and each node survives independently with a constant probability, the probability of having a subtree of surviving nodes of size Ω(log n) is at most ½.

In Self-Stabilization III session, *Toshimitsu Masuzawa*, a professor in Osaka University, presented the paper, “Edge Coloring Despite Transient and Permanent Faults”. In this paper, the authors provided a self-stabilizing algorithm, which colors the edges of an arbitrary graph so that every node has no two edges of the same color in the presence of Byzantine adversary and in ring topology. The basic idea is that coloring is performed in steps, where one node x proposes colors to its adjacent edges in one step. After setting these colors, if a neighboring node y has two incident edges of the same color, then node y proposes a different color to the edge (x, y). However, this kind of color proposals may not terminate in the presence of a Byzantine node. To overcome this problem, the authors used a rotating priority procedure, where each node has a priority to propose a color in case of conflict, and these priorities change in a round-robin fashion. Unfortunately, this algorithm does not color the graph with the minimum number of colors required. My consideration is that will their algorithm color the graph properly and terminate in case that there is a good node surrounded with two Byzantine nodes in a ring topology?

Also, *Hung Tran-The*, a graduate student in Universidade de Lisboa, presented his paper, “Tight Bounds for Stabilizing Uniform Consensus in Mobile Networks”. He provided a self-stabilizing algorithm, in which an agreement of nodes is obtained in the presence of crashes, send-omissions or general omissions. However, they claimed that there is no self-stabilizing algorithm in the presence of Byzantine adversary. This is arguable due to the existence of Byzantine Agreement. My consideration is that cannot we implement Byzantine agreement as a self-stabilizing algorithm?

Beside these scientific contents, I have a few comments about Paderborn city. Paderborn is a beautiful and quiet city in Germany. In this city, the mayor of Paderborn invited us to Paderborn Town-Hall. He gave us a presentation showing how beautiful Paderborn city is.

He told us that “Pader” of “Paderborn” means water spring, where Paderborn has many water springs.

We also visited a wonderful palace, Schloss *Corvey*, which is 57 km away from Paderborn.

Afterwards, we spent good time in a restaurant near to the palace.