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  • 1. Achilleos, Antonis
    et al.
    Lampis, Michail
    City University of New York.
    Mitsou, Valia
    Parameterized Modal Satisfiability2012In: Algorithmica, ISSN 0178-4617, E-ISSN 1432-0541, Vol. 64, no 1, p. 38-55Article in journal (Refereed)
    Abstract [en]

    We investigate the parameterized computational complexity of the satisfiability problem for modal logic and attempt to pinpoint relevant structural parameters which cause the problem’s combinatorial explosion, beyond the number of propositional variables v. To this end we study the modality depth, a natural measure which has appeared in the literature, and show that, even though modal satisfiability parameterized by v and the modality depth is FPT, the running time’s dependence on the parameters is a tower of exponentials (unless P=NP). To overcome this limitation we propose pos- sible alternative parameters, namely diamond dimension and modal width. We show fixed-parameter tractability results using these measures where the exponential dependence on the parameters is much milder (doubly and singly exponential respectively) than in the case of modality depth thus leading to FPT algorithms for modal satisfiability with much more reasonable running times. We also give lower bound arguments which prove that our algorithms cannot be improved significantly unless the Exponential Time Hypothesis fails.

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  • 2.
    Austrin, Per
    et al.
    KTH, School of Computer Science and Communication (CSC), Theoretical Computer Science, TCS.
    Chung, Kai-Min
    Mahmoody, Mohammad
    Pass, Rafael
    Seth, Karn
    On the Impossibility of Cryptography with Tamperable Randomness2017In: Algorithmica, ISSN 0178-4617, E-ISSN 1432-0541, Vol. 79, no 4, p. 1052-1101Article in journal (Refereed)
    Abstract [en]

    We initiate a study of the security of cryptographic primitives in the presence of efficient tampering attacks to the randomness of honest parties. More precisely, we consider p-tampering attackers that may efficiently tamper with each bit of the honest parties' random tape with probability p, but have to do so in an "online" fashion. Our main result is a strong negative result: We show that any secure encryption scheme, bit commitment scheme, or zero-knowledge protocol can be "broken" with advantage Omega(p) by a p-tampering attacker. The core of this result is a new algorithm for biasing the output of bounded-value functions, which may be of independent interest. We also show that this result cannot be extended to primitives such as signature schemes and identification protocols: assuming the existence of one-way functions, such primitives can be made resilient to (1/poly(n))-tampering attacks where n is the security parameter.

  • 3.
    Bansal, Nikhil
    et al.
    Eindhoven Univ Technol, Eindhoven, Netherlands..
    Chalermsook, Parinya
    Aalto Univ, Helsinki, Finland..
    Laekhanukit, Bundit
    Shanghai Univ Finance & Econ, Shanghai, Peoples R China..
    Na Nongkai, Danupon
    KTH, School of Electrical Engineering and Computer Science (EECS), Computer Science, Theoretical Computer Science, TCS.
    Nederlof, Jesper
    Eindhoven Univ Technol, Eindhoven, Netherlands..
    New Tools and Connections for Exponential-Time Approximation2019In: Algorithmica, ISSN 0178-4617, E-ISSN 1432-0541, Vol. 81, no 10, p. 3993-4009Article in journal (Refereed)
    Abstract [en]

    In this paper, we develop new tools and connections for exponential time approximation. In this setting, we are given a problem instance and an integer r > 1, and the goal is to design an approximation algorithm with the fastest possible running time. We give randomized algorithms that establish an approximation ratio of 1. r for maximum independent set in O*(exp((O) over tilde (n/r log(2) r + r log(2) r))) time, 2. r for chromatic number in O*(exp((O) over tilde (n/r log r + r log(2) r))) time, 3. (2 - 1/r) for minimum vertex cover in O*(exp(n/r(Omega(r)))) time, and 4. (k - 1/r) for minimum k-hypergraph vertex cover in O*(exp(n/(kr)(Omega(kr)))) time. (Throughout, (O) over tilde and O* omit polyloglog(r) and factors polynomial in the input size, respectively.) The best known time bounds for all problems were O*(2n/r) (Bourgeois et al. in Discret Appl Math 159(17): 1954-1970, 2011; Cygan et al. in Exponential-time approximation of hard problems, 2008). For maximum independent set and chromatic number, these bounds were complemented by exp(n(1-o(1))/r(1+o(1))) lower bounds (under the Exponential Time Hypothesis (ETH)) (Chalermsook et al. in Foundations of computer science, FOCS, pp. 370-379, 2013; Laekhanukit in Inapproximability of combinatorial problems in subexponential-time. Ph.D. thesis, 2014). Our results show that the naturally-looking O*(2n/r) bounds are not tight for all these problems. The key to these results is a sparsification procedure that reduces a problem to a bounded-degree variant, allowing the use of approximation algorithms for bounded-degree graphs. To obtain the first two results, we introduce a new randomized branching rule. Finally, we show a connection between PCP parameters and exponential-time approximation algorithms. This connection together with our independent set algorithm refute the possibility to overly reduce the size of Chan's PCP (Chan in J. ACM 63(3): 27: 1-27: 32, 2016). It also implies that a (significant) improvement over our result will refute the gap-ETH conjecture (Dinur in Electron Colloq Comput Complex (ECCC) 23: 128, 2016; Manurangsi and Raghavendra in A birthday repetition theorem and complexity of approximating dense CSPs, 2016).

  • 4.
    Bhangale, Amey
    et al.
    Department of Computer Science and Engineering, University of California, Riverside, USA.
    Stankovic, Aleksa
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Max-3-Lin Over Non-abelian Groups with Universal Factor Graphs2023In: Algorithmica, ISSN 0178-4617, E-ISSN 1432-0541, Vol. 85, no 9, p. 2693-2734Article in journal (Refereed)
    Abstract [en]

    The factor graph of an instance of a constraint satisfaction problem with n variables and m constraints is the bipartite graph between [m] and [n] describing which variable appears in which constraints. Thus, an instance of a CSP is completely determined by its factor graph and the list of predicates. We show optimal inapproximability of Max-3-LIN over non-Abelian groups (both in the perfect completeness case and in the imperfect completeness case), even when the factor graph is fixed. Previous reductions which proved similar optimal inapproximability results produced factor graphs that were dependent on the input instance. Along the way, we also show that these optimal hardness results hold even when we restrict the linear equations in the Max-3-LIN instances to the form x· y· z= g, where x, y, z are the variables and g is a group element. We use representation theory and Fourier analysis over non-Abelian groups to analyze the reductions.

  • 5.
    Bilò, Davide
    et al.
    University of Sassari.
    Böckenhauer, Hans-Joachim
    ETH Zurich.
    Komm, Dennis
    ETH Zurich.
    Kralovič, Richard
    ETH Zurich.
    Mömke, Tobias
    ETH Zurich.
    Seibert, Sebastian
    ETH Zurich.
    Zych, Anna
    ETH Zurich.
    Reoptimization of the Shortest Common Superstring Problem2011In: Algorithmica, ISSN 0178-4617, E-ISSN 1432-0541, Vol. 61, no 2, p. 227-251Article in journal (Refereed)
    Abstract [en]

    A reoptimization problem describes the following scenario: given aninstance of an optimization problem together with an optimal solution forit, we want to find a good solution for a locally modified instance.

    In this paper, we deal with reoptimization variants of the shortest commonsuperstring problem (SCS) where the local modifications consist of adding orremoving a single string.  We show the NP-hardness of thesereoptimization problems and design several approximation algorithms forthem. First, we use a technique of iteratively using any SCS algorithm todesign an approximation algorithm for the reoptimization variant of addinga string whose approximation ratio is arbitrarily close to 8/5 andanother algorithm for deleting a string with a ratio tending to 13/7. Bothalgorithms significantly improve over the best currently known SCSapproximation ratio of 2.5. Additionally, this iteration technique can be usedto design an improved SCS approximation algorithm (without reoptimization)if the input instance contains a long string, which might be of independentinterest. However, these iterative algorithms are relatively slow. Thus,we present another, faster approximation algorithm for inserting a stringwhich is based on cutting the given optimal solution and achieves anapproximation ratio of 11/6. Moreover, we give some lower bounds onthe approximation ratio which can be achieved by algorithms that use suchcutting strategies.

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  • 6.
    Bonacina, Ilario
    et al.
    KTH, School of Computer Science and Communication (CSC), Theoretical Computer Science, TCS.
    Talebanfard, Navid
    Strong ETH and Resolution via Games and the Multiplicity of Strategies2017In: Algorithmica, ISSN 0178-4617, E-ISSN 1432-0541, Vol. 79, no 1, p. 29-41Article in journal (Refereed)
    Abstract [en]

    We consider a proof system intermediate between regular Resolution, in which no variable can be resolved more than once along any refutation path, and general Resolution. We call -regular Resolution such system, in which at most a fraction of the variables can be resolved more than once along each refutation path (however, the re-resolved variables along different paths do not need to be the same). We show that when for not too large, -regular Resolution is consistent with the Strong Exponential Time Hypothesis (SETH). More precisely, for large n and k, we show that there are unsatisfiable k-CNF formulas which require -regular Resolution refutations of size , where n is the number of variables and and is the number of variables that can be resolved multiple times.

  • 7. Cai, Jin-Yi
    et al.
    Huang, Sangxia
    KTH, School of Computer Science and Communication (CSC), Theoretical Computer Science, TCS.
    Lu, Pinyan
    From Holant to #CSP and Back: Dichotomy for Holant (c) Problems2012In: Algorithmica, ISSN 0178-4617, E-ISSN 1432-0541, Vol. 64, no 3, p. 511-533Article in journal (Refereed)
    Abstract [en]

    We explore the intricate interdependent relationship among counting problems, considered from three frameworks for such problems: Holant Problems, counting CSP and weighted H-colorings. We consider these problems for general complex valued functions that take boolean inputs. We show that results from one framework can be used to derive results in another, and this happens in both directions. Holographic reductions discover an underlying unity, which is only revealed when these counting problems are investigated in the complex domain a",. We prove three complexity dichotomy theorems, leading to a general theorem for Holant (c) problems. This is the natural class of Holant problems where one can assign constants 0 or 1. More specifically, given any signature grid on G=(V,E) over a set of symmetric functions, we completely classify the complexity to be in P or #P-hard, according to F , of Sigma Pi f(v)(sigma vertical bar E(v)), sigma:E ->{0,1}v epsilon V where f(v) epsilon F boolean OR {0, 1} (0, 1 are the unary constant 0, 1 functions). Not only is holographic reduction the main tool, but also the final dichotomy can be only naturally stated in the language of holographic transformations. The proof goes through another dichotomy theorem on Boolean complex weighted #CSP.

  • 8.
    Nilsson, Stefan
    et al.
    KTH, Superseded Departments (pre-2005), Numerical Analysis and Computer Science, NADA.
    Tikkanen, A.
    An experimental study of compression methods for dynamic tries2002In: Algorithmica, ISSN 0178-4617, E-ISSN 1432-0541, Vol. 33, no 1, p. 19-33Article in journal (Refereed)
    Abstract [en]

    We study an order-preserving general purpose data structure for binary data, the LPC-trie. The structure is a compressed trie, using both level and path compression. The memory usage is similar to that of a balanced binary search tree, but the expected average depth is smaller. The LPC-trie is well suited to modem language environments with efficient memory allocation and garbage collection. We present an implementation in the Java programming language and show that the structure compares favorably with a balanced binary search tree.

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