An analytical framework for the performance evaluation of proximity-aware structured overlays

In this paper, we present an analytical study of proximity-aware structured peer-to-peer networks under churn. We use a master-equation-based approach, which is used traditionally in non-equilibrium statistical mechanics to describe steady-state or transient phenomena. In earlier work we have demonstrated that this methodology is in fact also well suited to describing structured overlay networks under churn, by showing how we can accurately predict the average number of hops taken by a lookup, for any value of churn, for the Chord system. In this paper, we extend the analysis so as to also be able to predict lookup latency, given an average latency for the links in the network. Our results show that there exists a region in the parameter space of the model, depending on churn, the number of nodes, the maintenance rates and the delays in the network, when the network cannot function as a small world graph anymore, due to the farthest connections of a node always being wrong or dead. We also demonstrate how it is possible to analyse proximity neighbour selection or proximity route selection within this formalism

Clustering of solutions in hard satisfiability problems

We study the structure of the solution space and behavior of local search methods on random 3-SAT problems close to the SAT/UNSAT transition. Using the overlap measure of similarity between different solutions found on the same problem instance we show that the solution space is shrinking as a function of alpha. We consider chains of satisfiability problems, where clauses are added sequentially. In each such chain, the overlap distribution is first smooth, and then develops a tiered structure, indicating that the solutions are found in well separated clusters. On chains of not too large instances, all solutions are eventually observed to be in only one small cluster before vanishing. This condensation transition point is estimated to be alpha_c = 4.26. The transition approximately obeys finite-size scaling with an apparent critical exponent of about 1.7. We compare the solutions found by a local heuristic, ASAT, and the Survey Propagation algorithm up to alpha_c.Comment: 8 pages, 9 figure

Behavior of heuristics and state space structure near SAT/UNSAT transition

We study the behavior of ASAT, a heuristic for solving satisfiability problems by stochastic local search near the SAT/UNSAT transition. The heuristic is focused, i.e. only variables in unsatisfied clauses are updated in each step, and is significantly simpler, while similar to, walksat or Focused Metropolis Search. We show that ASAT solves instances as large as one million variables in linear time, on average, up to 4.21 clauses per variable for random 3SAT. For K higher than 3, ASAT appears to solve instances at the ``FRSB threshold'' in linear time, up to K=7.Comment: 12 pages, 6 figures, longer version available as MSc thesis of first author at http://biophys.physics.kth.se/docs/ardelius_thesis.pd

Exhaustive enumeration unveils clustering and freezing in random 3-SAT

We study geometrical properties of the complete set of solutions of the random 3-satisfiability problem. We show that even for moderate system sizes the number of clusters corresponds surprisingly well with the theoretic asymptotic prediction. We locate the freezing transition in the space of solutions which has been conjectured to be relevant in explaining the onset of computational hardness in random constraint satisfaction problems.Comment: 4 pages, 3 figure

On state space structure and average case complexity in random K-SAT problems

This thesis gives an introduction to a currently active area in the cross-section between theoretical computer science and theoretical physics. In the last ten years it has been suggested that critical behaviour, usually seen in models from condensed matter physics, may be responsible for the intractability of NP complete computation problems. This would suggest a very deep connection between the two fields on the most fundamental level. How deep this connection really is is subject to ongoing research as well as the topic of this thesis. Some of the conjectrues from the physics community regarding computational hardness in certain problem classes has turned out to be wrong or misinterpreted but the gained interest in both fields has promising potiential in moving the research frontier forward. The material presented in this thesis is the result of nearly two years work in trying to clearify how the results from physics can be interpreted in the language of actuall computation problems.Denna avhandling ger en introduktion till ett mycket aktivt forskningsområde i gränslandet mellan teortisk datalogi och teoretisk fysik. Under de senaste tio åren har det framkommit forskningsresultat som pekar på att kritiska fenomen, vanligen hemmahörande i modeller från teoretisk materialfysik, kan vara nyckeln till att förstå varför NP fullständiga problem är så svåra att lösa. Detta skulle innebära en mycket djup och fundamental koppling mellan de bägge områdena. Hur djup denna koppling verkligen är är temat i mycket av pågående forskning såväl som ämnet för denna avhandling. Vissa förutsägelser från den teoretiska fysiken har visat sig felaktiga eller feltolkade men det ökade intresset för dylika frågor inom bägge forskningområden ger hopp om att tillsammans kunna flytta from forskningsfronten.QC 2010110

On the Performance Analysis of Large Scale, Dynamic, Distributed and Parallel Systems.

Evaluating the performance of large distributed applications is an important and non-trivial task. With the onset of Internet wide applications there is an increasing need to quantify reliability, dependability and performance of these systems, both as a guide in system design as well as a means to understand the fundamental properties of large-scale distributed systems. Previous research has mainly focused on either formalised models where system properties can be deduced and verified using rigorous mathematics or on measurements and experiments on deployed applications. Our aim in this thesis is to study models on an abstraction level lying between the two ends of this spectrum. We adopt a model of distributed systems inspired by methods used in the study of large scale system of particles in physics and model the application nodes as a set of interacting particles each with an internal state whose actions are specified by the application program. We apply our modeling and performance evaluation methodology to four different distributed and parallel systems. The first system is the distributed hash table (DHT) Chord running in a dynamic environment.  We study the system under two scenarios. First we study how performance (in terms of lookup latency) is affectedon a network with finite communication latency. We show that an average delay in conjunction with other parameters describing changes in the network (such as timescales for network repair and join and leave processes)induces fundamentally different system performance. We also verify our analytical predictions via simulations.In the second scenario we introduce network address translators (NATs) to the network model. This makes the overlay topology non-transitive and we explore the implications of this fact to various performance metrics such as lookup latency, consistency and load balance. The latter analysis is mainly simulation based.Even though these two studies focus on a specific DHT, many of our results can easily be translated to other similar ring-based DHTs with long-range links, and the same methodology can be applied evento DHT's based on other geometries.The second type of system studied is an unstructured gossip protocol running a distributed version of the famous Belman-Ford algorithm. The algorithm, called GAP, generates a spanning tree over the participating nodes and the question we set out to study is how reliable this structure is(in terms of generating accurate aggregate values at the root)  in the presence of node churn. All our analytical results are also verified  using simulations.The third system studied is a content distribution network (CDN) of interconnected caches in an aggregation access network. In this model, content which sits at the leaves of the cache hierarchy tree, is requested by end users. Requests can then either be served by the first cache level or sent further up the tree. We study the performance of the whole system under two cache eviction policies namely LRU and LFU. We compare our analytical results with traces from related caching systems.The last system is a work stealing heuristic for task distribution in the TileraPro64 chip. This system has access to a shared memory and is therefore classified as a parallel system. We create a model for the dynamic generation of tasks as well as how they are executed and distributed among the participating nodes. We study how the heuristic scales when the number of nodes exceeds the number of processors on the chip as well as how different work stealing policies compare with each other. The work on this model is mainly simulation-based.Att utvärdera prestanda hos storskaliga distribuerade system är en viktigoch icke-trivial uppgift. I och med utvecklingen av Internet och det faktum attapplikationer och system har fått global utsträckning, har det uppkommit ettökande behov av kvantifiering av tillförlitlighet och prestanda hos dessa system.Både som underlag för systemdesign men också för att skapa förståelseoch kunskap om fundamentala egenskaper hos distribuerade system.Tidigare forskning har i mångt och mycket fokuserat antingen på formaliserademodeller, där egenskaper kan härledas med hjälp av strikta matematiskametoder eller på mätningar av riktiga system. Målet med arbetet i dennaavhandling är att undersöka modeller på en abstraktionsnivå mellan dessa tvåytterligheter. Vi tillämpar en modell av distributerade system med inspirationfrån så kallade partikelmodeller från den teoretiska fysiken och modellererarapplikationsnoder som en samling interagerande pariklar var och en med sitteget interna tillstånd vars beteende beskrivs av det exekvernade programmeti fråga. Vi tillämpar denna modelerings- och utvärderingsmetod på fyra olikadistribuerade och parallella system.Det första systemet är den distribuerade hash tabellen (DHT) Chord i endynamisk miljö. Vi har valt att studera systemet under två scenarion. Förstutvärderar vi hur systemet beteer sig (med avseende på lookup latency) iett nätverk med finita kommunikationsfördröjningar. Vårt arbete visar atten generell fördröjning i nätet tillsammans med andra parametrar (som t.ex.tidsskala för felkorrektion och anslutningsprocess för noder) genererar fundamentaltskilda prestandamått. Vi verifierar vår analytiska model med simuleringar.I det andra scenariot undersöker vi betydelsen av NATs (networkadress translators) i nätverksmodellen. Förekomsten av dessa tar bort dentransitiva egenskapen hos nätverkstopologin och vi undersöker hur detta påverkarlookup-kostnad, datakonsistens och lastbalans. Denna analys är främst simuleringsbaserad.Även om dessa två studier fokuserar på en specifik DHT såkan de flesta resultat och metoden som sådan överföras på andra liknanderingbaserade DHTer med långa länkar och även andra geometrier.Den andra klassen av system som analyseras är ostrukturerade gossip protokolli form av den välkända Belman-Ford algoritmen. Algoritmen, GAP,skapar ett spännande träd över systemets noder. Problemställningen vi studerarär hur tillförlitlig denna struktur, med avseende på precisionen på aggregatvid rotnoden, är i ett dynamiskt nätverk. Samtliga analytiska resultatverifieras i simulator.Det tredje systemet vi undersöker är ett CDN (content distribution system)med en hierarkisk cache struktur i sitt distributionsnät. I den här modellenefterfrågas data från löven på cache-trädet. Antingen kan förfrågan servas avcacharna på de lägre nivåerna eller så skickas förfrågan vidare uppåt i trädet.Vi analyserar två fundamentala heuristiker, LRU och LFU. Vi jämför våraanalytiska resultat med tracedata från riktiga cachesystem.Till sist analyserar vi en heuristik för last distribution i TileraPro64 arkitekturen.Systemet har ett centralt delat minne och är därför att betrakta somparallellt. Vi skapar här en model för den dynamiska genereringen av lastsamt hur denna distribueras till de olika noderna på chipet. Vi studerar hur heuristiken skalar när antalet noder överstiger antalet på chipet (64) samtjämför prestanda hos olika heuristiker. Analysen är simuleringsbaserad.QC 20131128</p

On state space structure and average case complexity in random K-SAT problems

This thesis gives an introduction to a currently active area in the cross-section between theoretical computer science and theoretical physics. In the last ten years it has been suggested that critical behaviour, usually seen in models from condensed matter physics, may be responsible for the intractability of NP complete computation problems. This would suggest a very deep connection between the two fields on the most fundamental level. How deep this connection really is is subject to ongoing research as well as the topic of this thesis. Some of the conjectrues from the physics community regarding computational hardness in certain problem classes has turned out to be wrong or misinterpreted but the gained interest in both fields has promising potiential in moving the research frontier forward. The material presented in this thesis is the result of nearly two years work in trying to clearify how the results from physics can be interpreted in the language of actuall computation problems.Denna avhandling ger en introduktion till ett mycket aktivt forskningsområde i gränslandet mellan teortisk datalogi och teoretisk fysik. Under de senaste tio åren har det framkommit forskningsresultat som pekar på att kritiska fenomen, vanligen hemmahörande i modeller från teoretisk materialfysik, kan vara nyckeln till att förstå varför NP fullständiga problem är så svåra att lösa. Detta skulle innebära en mycket djup och fundamental koppling mellan de bägge områdena. Hur djup denna koppling verkligen är är temat i mycket av pågående forskning såväl som ämnet för denna avhandling. Vissa förutsägelser från den teoretiska fysiken har visat sig felaktiga eller feltolkade men det ökade intresset för dylika frågor inom bägge forskningområden ger hopp om att tillsammans kunna flytta from forskningsfronten.QC 2010110