Search

In many traditional job scheduling settings, it is assumed that one knows the time it will take for a job to complete service. In such cases, strategies such as shortest job first can be used to improve performance in terms of measures such as the average time a job waits in the system. We consider the setting where the service time is not known, but is predicted by for example a machine learning algorithm. Our main result is the derivation, under natural assumptions, of formulae for the performance of several strategies for queueing systems that use predictions for service times in order to schedule jobs. As part of our analysis, we suggest the framework of the "price of misprediction," which offers a measure of the cost of using predicted information., 14 pages, submitted; version 2 has updated references, some corrections

In a $k$-party communication problem, the $k$ players with inputs $x_1, x_2, \ldots, x_k$, respectively, want to evaluate a function $f(x_1, x_2, \ldots, x_k)$ using as little communication as possible. We consider the message-passing model, in which the inputs are partitioned in an arbitrary, possibly worst-case manner, among a smaller number $t$ of players ($t, Comment: Preliminary version appeared in ICALP 2019, submitted to ToC

Front Matter, Table of Contents, Preface, Conference Organization

This report documents the program and the topics discussed of the 4-day Dagstuhl Seminar 17181 "Theory and Applications of Hashing", which took place May 1-5, 2017. Four long and eighteen short talks covered a wide and diverse range of topics within the theme of the workshop. The program left sufficient space for informal discussions among the 40 participants.

We study novel variations of Voronoi games and associated random processes that we call Voronoi choice games. These games provide a rich framework for studying questions regarding the power of small numbers of choices in multi-player, competitive scenarios, and they further lead to many interesting, non-trivial random processes that appear worthy of study. As an example of the type of problem we study, suppose a group of $n$ miners are staking land claims through the following process: each miner has $m$ associated points independently and uniformly distributed on an underlying space, so the $k$th miner will have associated points $p_{k1},p_{k2},\ldots,p_{km}$. Each miner chooses one of these points as the base point for their claim. Each miner obtains mining rights for the area of the square that is closest to their chosen base, that is, they obtain the Voronoi cell corresponding to their chosen point in the Voronoi diagram of the $n$ chosen points. Each player's goal is simply to maximize the amount of land under their control. What can we say about the players' strategy and the equilibria of such games? In our main result, we derive bounds on the expected number of pure Nash equilibria for a variation of the 1-dimensional game on the circle where a player owns the arc starting from their point and moving clockwise to the next point. This result uses interesting properties of random arc lengths on circles, and demonstrates the challenges in analyzing these kinds of problems. We also provide several other related results. In particular, for the 1-dimensional game on the circle, we show that a pure Nash equilibrium always exists when each player owns the part of the circle nearest to their point, but it is NP-hard to determine whether a pure Nash equilibrium exists in the variant when each player owns the arc starting from their point clockwise to the next point.

Front Matter, Table of Contents, Preface, Organization, List of Authors

International audience; We prove the first Chernoff-Hoeffding bounds for general nonreversible finite-state Markov chains based on the standard L_1 (variation distance) mixing-time of the chain. Specifically, consider an ergodic Markov chain M and a weight function f: [n] -> [0,1] on the state space [n] of M with mean mu = E_{v = delta mu t ], is at most exp(-Omega( delta^2 mu t / T )) for 0 1. In fact, the bounds hold even if the weight functions f_i's for i in [t] are distinct, provided that all of them have the same mean mu. We also obtain a simplified proof for the Chernoff-Hoeffding bounds based on the spectral expansion lambda of M, which is the square root of the second largest eigenvalue (in absolute value) of M tilde{M}, where tilde{M} is the time-reversal Markov chain of M. We show that the probability Pr [ |X - mu t| >= delta mu t ] is at most exp(-Omega( delta^2 (1-lambda) mu t )) for 0 1. Both of our results extend to continuous-time Markov chains, and to the case where the walk starts from an arbitrary distribution x, at a price of a multiplicative factor depending on the distribution x in the concentration bounds.

International audience; In their seminal work, Alon, Matias, and Szegedy introduced several sketching techniques, including showing that 4-wise independence is sufficient to obtain good approximations of the second frequency moment. In this work, we show that their sketching technique can be extended to product domains $[n]^k$ by using the product of 4-wise independent functions on $[n]$. Our work extends that of Indyk and McGregor, who showed the result for $k = 2$. Their primary motivation was the problem of identifying correlations in data streams. In their model, a stream of pairs $(i,j) \in [n]^2$ arrive, giving a joint distribution $(X,Y)$, and they find approximation algorithms for how close the joint distribution is to the product of the marginal distributions under various metrics, which naturally corresponds to how close $X$ and $Y$ are to being independent. By using our technique, we obtain a new result for the problem of approximating the $\ell_2$ distance between the joint distribution and the product of the marginal distributions for $k$-ary vectors, instead of just pairs, in a single pass. Our analysis gives a randomized algorithm that is a $(1 \pm \epsilon)$ approximation (with probability $1-\delta$) that requires space logarithmic in $n$ and $m$ and proportional to $3^k$.

We consider asymmetric convex intersection testing (ACIT). Let P subset R^d be a set of n points and H a set of n halfspaces in d dimensions. We denote by {ch(P)} the polytope obtained by taking the convex hull of P, and by {fh(H)} the polytope obtained by taking the intersection of the halfspaces in H. Our goal is to decide whether the intersection of H and the convex hull of P are disjoint. Even though ACIT is a natural variant of classic LP-type problems that have been studied at length in the literature, and despite its applications in the analysis of high-dimensional data sets, it appears that the problem has not been studied before. We discuss how known approaches can be used to attack the ACIT problem, and we provide a very simple strategy that leads to a deterministic algorithm, linear on n and m, whose running time depends reasonably on the dimension d., OpenAccess Series in Informatics (OASIcs), 69, ISSN:2190-6807, 2nd Symposium on Simplicity in Algorithms (SOSA 2019), ISBN:978-3-95977-099-6

We consider a problem of searching for an unknown target vertex t in a (possibly edge-weighted) graph. Each vertex-query points to a vertex v and the response either admits that v is the target or provides any neighbor s of v that lies on a shortest path from v to t. This model has been introduced for trees by Onak and Parys [FOCS 2006] and for general graphs by Emamjomeh-Zadeh et al. [STOC 2016]. In the latter, the authors provide algorithms for the error-less case and for the independent noise model (where each query independently receives an erroneous answer with known probability p, OpenAccess Series in Informatics (OASIcs), 69, ISSN:2190-6807, 2nd Symposium on Simplicity in Algorithms (SOSA 2019), ISBN:978-3-95977-099-6

In a recent breakthrough, Paz and Schwartzman (SODA'17) presented a single-pass (2+epsilon)-approximation algorithm for the maximum weight matching problem in the semi-streaming model. Their algorithm uses O(n log^2 n) bits of space, for any constant epsilon>0. We present a simplified and more intuitive primal-dual analysis, for essentially the same algorithm, which also improves the space complexity to the optimal bound of O(n log n) bits - this is optimal as the output matching requires Omega(n log n) bits., OpenAccess Series in Informatics (OASIcs), 69, ISSN:2190-6807, 2nd Symposium on Simplicity in Algorithms (SOSA 2019), ISBN:978-3-95977-099-6

Plurality consensus considers a network of n nodes, each having one of k opinions. Nodes execute a (randomized) distributed protocol with the goal that all nodes adopt the plurality (the opinion initially supported by the most nodes). Communication is realized via the Gossip (or random phone call) model. A major open question has been whether there is a protocol for the complete graph that converges (w.h.p.) in polylogarithmic time and uses only polylogarithmic memory per node (local memory). We answer this question affirmatively. We propose two protocols that need only mild assumptions on the bias in favor of the plurality. As an example of our results, consider the complete graph and an arbitrarily small constant multiplicative bias in favor of the plurality. Our first protocol achieves plurality consensus in O(log(k)*log(log(n))) rounds using log(k) + Theta(log(log(k))) bits of local memory. Our second protocol achieves plurality consensus in O(log(n)*log(log(n))) rounds using only log(k) + 4 bits of local memory. This disproves a conjecture by Becchetti et al. (SODA'15) implying that any protocol with local memory log(k)+O(1) has worst-case runtime Omega(k). We provide similar bounds for much weaker bias assumptions. At the heart of our protocols lies an undecided state, an idea introduced by Angluin et al. (Distributed Computing'08).

Many real-life planning problems require making a priori decisions before all parameters of the problem have been revealed. An important special case of such problem arises in scheduling and transshipment problems, where a set of jobs needs to be assigned to the available set of machines or personnel (resources), in a way that all jobs have assigned resources, and no two jobs share the same resource. In its nominal form, the resulting computational problem becomes the assignment problem. This paper deals with the Robust Assignment Problem (RAP) which models situations in which certain assignments are vulnerable and may become unavailable after the solution has been chosen. The goal is to choose a minimum-cost collection of assignments (edges in the corresponding bipartite graph) so that if any vulnerable edge becomes unavailable, the remaining part of the solution contains an assignment of all jobs. We develop algorithms and hardness results for RAP and establish several connections to well-known concepts from matching theory, robust optimization, LP-based techniques and combinations thereof., Leibniz International Proceedings in Informatics (LIPIcs), 55, ISSN:1868-8969, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016), ISBN:978-3-95977-013-2

An adjacency labeling scheme labels the n nodes of a graph with bit strings in a way that allows, given the labels of two nodes, to determine adjacency based only on those bit strings. Though many graph families have been meticulously studied for this problem, a non-trivial labeling scheme for the important family of power-law graphs has yet to be obtained. This family is particularly useful for social and web networks as their underlying graphs are typically modelled as power-law graphs. Using simple strategies and a careful selection of a parameter, we show upper bounds for such labeling schemes of ~O(sqrt^{alpha}(n)) for power law graphs with coefficient alpha;, as well as nearly matching lower bounds. We also show two relaxations that allow for a label of logarithmic size, and extend the upper-bound technique to produce an improved distance labeling scheme for power-law graphs.

Herman's self-stabilisation algorithm, introduced 25 years ago, is a well-studied synchronous randomised protocol for enabling a ring of $N$ processes collectively holding any odd number of tokens to reach a stable state in which a single token remains. Determining the worst-case expected time to stabilisation is the central outstanding open problem about this protocol. It is known that there is a constant $h$ such that any initial configuration has expected stabilisation time at most $h N^2$. Ten years ago, McIver and Morgan established a lower bound of $4/27 \approx 0.148$ for $h$, achieved with three equally-spaced tokens, and conjectured this to be the optimal value of $h$. A series of papers over the last decade gradually reduced the upper bound on $h$, with the present record (achieved in 2014) standing at approximately $0.156$. In this paper, we prove McIver and Morgan's conjecture and establish that $h = 4/27$ is indeed optimal., ICALP 2016

We consider the problem of computing a $(1+\epsilon)$-approximation of the Hamming distance between a pattern of length $n$ and successive substrings of a stream. We first look at the one-way randomised communication complexity of this problem, giving Alice the first half of the stream and Bob the second half. We show the following: (1) If Alice and Bob both share the pattern then there is an $O(\epsilon^{-4} \log^2 n)$ bit randomised one-way communication protocol. (2) If only Alice has the pattern then there is an $O(\epsilon^{-2}\sqrt{n}\log n)$ bit randomised one-way communication protocol. We then go on to develop small space streaming algorithms for $(1+\epsilon)$-approximate Hamming distance which give worst case running time guarantees per arriving symbol. (1) For binary input alphabets there is an $O(\epsilon^{-3} \sqrt{n} \log^{2} n)$ space and $O(\epsilon^{-2} \log{n})$ time streaming $(1+\epsilon)$-approximate Hamming distance algorithm. (2) For general input alphabets there is an $O(\epsilon^{-5} \sqrt{n} \log^{4} n)$ space and $O(\epsilon^{-4} \log^3 {n})$ time streaming $(1+\epsilon)$-approximate Hamming distance algorithm., Comment: Submitted to ICALP' 2016

We study data structure problems related to document indexing and pattern matching queries and our main contribution is to show that the pointer machine model of computation can be extremely useful in proving high and unconditional lower bounds that cannot be obtained in any other known model of computation with the current techniques. Often our lower bounds match the known space-query time trade-off curve and in fact for all the problems considered, there is a very good and reasonable match between the our lower bounds and the known upper bounds, at least for some choice of input parameters. The problems that we consider are set intersection queries (both the reporting variant and the semi-group counting variant), indexing a set of documents for two-pattern queries, or forbidden- pattern queries, or queries with wild-cards, and indexing an input set of gapped-patterns (or two-patterns) to find those matching a document given at the query time., Comment: Full version of the conference version that appeared at ICALP 2016, 25 pages

Conditional lower bounds for dynamic graph problems has received a great deal of attention in recent years. While many results are now known for the fully-dynamic case and such bounds often imply worst-case bounds for the partially dynamic setting, it seems much more difficult to prove amortized bounds for incremental and decremental algorithms. In this paper we consider partially dynamic versions of three classic problems in graph theory. Based on popular conjectures we show that: -- No algorithm with amortized update time $O(n^{1-\varepsilon})$ exists for incremental or decremental maximum cardinality bipartite matching. This significantly improves on the $O(m^{1/2-\varepsilon})$ bound for sparse graphs of Henzinger et al. [STOC'15] and $O(n^{1/3-\varepsilon})$ bound of Kopelowitz, Pettie and Porat. Our linear bound also appears more natural. In addition, the result we present separates the node-addition model from the edge insertion model, as an algorithm with total update time $O(m\sqrt{n})$ exists for the former by Bosek et al. [FOCS'14]. -- No algorithm with amortized update time $O(m^{1-\varepsilon})$ exists for incremental or decremental maximum flow in directed and weighted sparse graphs. No such lower bound was known for partially dynamic maximum flow previously. Furthermore no algorithm with amortized update time $O(n^{1-\varepsilon})$ exists for directed and unweighted graphs or undirected and weighted graphs. -- No algorithm with amortized update time $O(n^{1/2 - \varepsilon})$ exists for incremental or decremental $(4/3-\varepsilon')$-approximating the diameter of an unweighted graph. We also show a slightly stronger bound if node additions are allowed. [...], Comment: To appear at ICALP'16. Abstract truncated to fit arXiv limits

Protecting software from malware injection is one of the biggest challenges of modern computer science. Despite intensive efforts by the scientific and engineering community, the number of successful attacks continues to increase. This work sets first footsteps towards a provably secure investigation of malware detection. We provide a formal model and cryptographic security definitions of attestation for systems with dynamic memory, and suggest novel provably secure attestation schemes. The key idea underlying our schemes is to use the very insertion of the malware itself to allow for the systems to detect it. This is, in our opinion, close in spirit to the quantum Observer Effect. The attackers, no matter how clever, no matter when they insert their malware, change the state of the system they are attacking. This fundamental idea can be a game changer. And our system does not rely on heuristics; instead, our scheme enjoys the unique property that it is proved secure in a formal and precise mathematical sense and with minimal and realistic CPU modification achieves strong provable security guarantees. We envision such systems with a formal mathematical security treatment as a venue for new directions in software protection.

Geometric inhomogeneous random graphs (GIRGs) are a model for scale-free networks with underlying geometry. We study bootstrap percolation on these graphs, which is a process modelling the spread of an infection of vertices starting within a (small) local region. We show that the process exhibits a phase transition in terms of the initial infection rate in this region. We determine the speed of the process in the supercritical case, up to lower order terms, and show that its evolution is fundamentally influenced by the underlying geometry. For vertices with given position and expected degree, we determine the infection time up to lower order terms. Finally, we show how this knowledge can be used to contain the infection locally by removing relatively few edges from the graph. This is the first time that the role of geometry on bootstrap percolation is analysed mathematically for geometric scale-free networks., Leibniz International Proceedings in Informatics (LIPIcs), 55, ISSN:1868-8969, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016), ISBN:978-3-95977-013-2

The dual graph model describes a radio network that contains both reliable and unreliable links. In recent years, this model has received significant attention by the distributed algorithms community [Kuhn/Lynch/Newport/Oshman/Richa, PODC 2010; Censor-Hillel/Gilbert/Kuhn/Lynch/Newport, Dist. Comp. 2014; Ghaffari/Haeupler/Lynch/Newport, DISC 2012; Ghaffari/Lynch/Newport, PODC 2013; Ghaffir/Kantor/Lynch/Newport, PODC 2014; Newport, DISC 2014; Ahmadi/Ghodselahi/Kuhn/Molla, OPODIS 2015; Lynch/Newport, PODC 2015]. Due to results in [Ghaffari/Lynch/Newport, PODC 2013], it is known that leader election plays a key role in enabling efficient computation in this difficult setting: a leader can synchronize the network in such a manner that most problems can be subsequently solved in time similar to the classical radio network model that lacks unreliable links. The feasibility of efficient leader election in the dual graph model, however, was left as an important open question. In this paper, we answer this question. In more detail, we prove new upper and lower bound results that characterize the complexity of leader election in this setting. By doing so, we reveal a surprising dichotomy: (1) under the assumption that the network size n is in the range 1 to N, where N is a large upper bound on the maximum possible network size (e.g., the ID space), leader election is fundamentally hard, requiring ~Omega(sqrt(N)) rounds to solve in the worst-case; (2) under the assumption that n is in the range 2 to N, however, the problem can be solved in only ~O(D) rounds, for network diameter D, matching the lower bound for leader election in the standard radio network model (within log factors) [Ghaffari/Haeupler, SODA 2013]., Leibniz International Proceedings in Informatics (LIPIcs), 55, ISSN:1868-8969, 43rd International Colloquium on Automata, Languages, and Programming, ISBN:978-3-95977-013-2

We provide simple but surprisingly useful direct product theorems for proving lower bounds on online algorithms with a limited amount of advice about the future. Intuitively, our direct product theorems say that if b bits of advice are needed to ensure a cost of at most t for some problem, then r*b bits of advice are needed to ensure a total cost of at most r*t when solving r independent instances of the problem. Using our direct product theorems, we are able to translate decades of research on randomized online algorithms to the advice complexity model. Doing so improves significantly on the previous best advice complexity lower bounds for many online problems, or provides the first known lower bounds. For example, we show that - A paging algorithm needs Omega(n) bits of advice to achieve a competitive ratio better than H_k = Omega(log k), where k is the cache size. Previously, it was only known that Omega(n) bits of advice were necessary to achieve a constant competitive ratio smaller than 5/4. - Every O(n^{1-epsilon})-competitive vertex coloring algorithm must use Omega(n log n) bits of advice. Previously, it was only known that Omega(n log n) bits of advice were necessary to be optimal. For certain online problems, including the MTS, k-server, metric matching, paging, list update, and dynamic binary search tree problem, we prove that randomization and sublinear advice are equally powerful (if the underlying metric space or node set is finite). This means that several long-standing open questions regarding randomized online algorithms can be equivalently stated as questions regarding online algorithms with sublinear advice. For example, we show that there exists a deterministic O(log k)-competitive k-server algorithm with sublinear advice if and only if there exists a randomized O(log k)-competitive k-server algorithm without advice. Technically, our main direct product theorem is obtained by extending an information theoretical lower bound technique due to Emek, Fraigniaud, Korman, and Rosén [ICALP'09].

For $n\geq 3$, let $(H_n, E)$ denote the $n$-th Henson graph, i.e., the unique countable homogeneous graph with exactly those finite graphs as induced subgraphs that do not embed the complete graph on $n$ vertices. We show that for all structures $\Gamma$ with domain $H_n$ whose relations are first-order definable in $(H_n,E)$ the constraint satisfaction problem for $\Gamma$ is either in P or is NP-complete. We moreover show a similar complexity dichotomy for all structures whose relations are first-order definable in a homogeneous graph whose reflexive closure is an equivalence relation. Together with earlier results, in particular for the random graph, this completes the complexity classification of constraint satisfaction problems of structures first-order definable in countably infinite homogeneous graphs: all such problems are either in P or NP-complete., Comment: 41 pages