Near-linear Time Algorithm for Approximate Minimum Degree Spanning Trees

Given a graph $G = (V, E)$, we wish to compute a spanning tree whose maximum vertex degree, i.e. tree degree, is as small as possible. Computing the exact optimal solution is known to be NP-hard, since it generalizes the Hamiltonian path problem. For the approximation version of this problem, a $\tilde{O}(mn)$ time algorithm that computes a spanning tree of degree at most $\Delta^* +1$ is previously known [F\"urer \& Raghavachari 1994]; here $\Delta^*$ denotes the minimum tree degree of all the spanning trees. In this paper we give the first near-linear time approximation algorithm for this problem. Specifically speaking, we propose an $\tilde{O}(\frac{1}{\epsilon^7}m)$ time algorithm that computes a spanning tree with tree degree $(1+\epsilon)\Delta^* + O(\frac{1}{\epsilon^2}\log n)$ for any constant $\epsilon \in (0,\frac{1}{6})$. Thus, when $\Delta^*=\omega(\log n)$, we can achieve approximate solutions with constant approximate ratio arbitrarily close to 1 in near-linear time.Comment: 17 page

Improved Algorithm for Degree Bounded Survivable Network Design Problem

We consider the Degree-Bounded Survivable Network Design Problem: the objective is to find a minimum cost subgraph satisfying the given connectivity requirements as well as the degree bounds on the vertices. If we denote the upper bound on the degree of a vertex v by b(v), then we present an algorithm that finds a solution whose cost is at most twice the cost of the optimal solution while the degree of a degree constrained vertex v is at most 2b(v) + 2. This improves upon the results of Lau and Singh and that of Lau, Naor, Salavatipour and Singh

TRAVEL WATTLE OF LANDSCAPES, ANTIQUITY AND SPIRITUAL AURA OF SPACE IN TRAVELOGUES BY ZLATKO TOMIČIĆ

U radu se prvi put revalorizira još posve neistražen književni opus tiskanih putopisnih zbirka istaknutoga suvremenog hrvatskog književnika Zlatka Tomičića (Zagreb, 1930. – Zagreb, 2008.). Današnja međunarodna književna produkcija snažno je usmjerena prema oblikovanjima tzv. nefikcionalnih žanrova (memoara, putopisa, autobiografija) pa se prema ulozi reanimiranja misaonoga poklisara realiziraju i Tomičićevi putopisi. Tomičićeva putopisna proza jednim se dijelom promatra u kontekstu njegovih književnih suvremenika i političko-društvene sudbine autora. Međutim rad se u prvome planu usmjerava na književnu analizu i interpretaciju šesnaest putopisnih knjiga te se unutar autorova oblikotvornoga postupka promatraju i njegovi književni utjecaji, književne relacije i refleksivno-filozofski obzori. Bitna konstanta Tomičićeva putopisa jest težnja za polifonijskim i polihistorijskim modelom doživljavanja svijeta. Kao obilježje Tomičićeva umjetničkoga postupka izdvaja se interferencijska realizacija hibridnoga žanra putopisa i stvaranje književnoga pletera, tj. ispreplitanja kozmopolitizma i rodoljublja te povezivanja realističkih zapažanja s konstantom kulturno-duhovne aure opisivanoga prostora.The paper valorizes for the first time a completely unexplored literary opus of published travelogue collections of prominent contemporary Croatian writer Zlatko Tomičić (Zagreb, 1930. – Zagreb, 2008.). Contemporary international literary production is strongly directed to forming of the so called non-fictional genres (memoirs, travelogues, autobiographies), therefore Tomičić’s travelogues are also realized in accordance with the role of reanimating contemplative envoy. Tomičić’s travel prose is partly considered in the context of his literary contemporaries and authors’ political-social destiny. However, the paper is in the first plan directed to literary analysis and interpretation of sixteen travelogues and author’s literary influences, literary relations and reflexive-philosophic visions are considered within his forming procedure. A very important constant of author’s travelogue is aspiration to polyphonic and historic model of life experiencing. The characteristic of Tomičić’s artistic procedure is interferential realization of hybrid travelogue genre and creation of literary wattle i.e. interweaving of cosmopolitism and patriotism and connecting of realistic observations with a constant of cultural-spiritual aura of described space

An Efficient Local Search for Partial Latin Square Extension Problem

A partial Latin square (PLS) is a partial assignment of n symbols to an nxn grid such that, in each row and in each column, each symbol appears at most once. The partial Latin square extension problem is an NP-hard problem that asks for a largest extension of a given PLS. In this paper we propose an efficient local search for this problem. We focus on the local search such that the neighborhood is defined by (p,q)-swap, i.e., removing exactly p symbols and then assigning symbols to at most q empty cells. For p in {1,2,3}, our neighborhood search algorithm finds an improved solution or concludes that no such solution exists in O(n^{p+1}) time. We also propose a novel swap operation, Trellis-swap, which is a generalization of (1,q)-swap and (2,q)-swap. Our Trellis-neighborhood search algorithm takes O(n^{3.5}) time to do the same thing. Using these neighborhood search algorithms, we design a prototype iterated local search algorithm and show its effectiveness in comparison with state-of-the-art optimization solvers such as IBM ILOG CPLEX and LocalSolver.Comment: 17 pages, 2 figure

Hamiltonian Cycle Parameterized by Treedepth in Single Exponential Time and Polynomial Space

For many algorithmic problems on graphs of treewidth $t$, a standard dynamic programming approach gives an algorithm with time and space complexity $2^{\mathcal{O}(t)}\cdot n^{\mathcal{O}(1)}$. It turns out that when one considers the more restrictive parameter treedepth, it is often the case that a variation of this technique can be used to reduce the space complexity to polynomial, while retaining time complexity of the form $2^{\mathcal{O}(d)}\cdot n^{\mathcal{O}(1)}$, where $d$ is the treedepth. This transfer of methodology is, however, far from automatic. For instance, for problems with connectivity constraints, standard dynamic programming techniques give algorithms with time and space complexity $2^{\mathcal{O}(t\log t)}\cdot n^{\mathcal{O}(1)}$ on graphs of treewidth $t$, but it is not clear how to convert them into time-efficient polynomial space algorithms for graphs of low treedepth. Cygan et al. (FOCS'11) introduced the Cut&Count technique and showed that a certain class of problems with connectivity constraints can be solved in time and space complexity $2^{\mathcal{O}(t)}\cdot n^{\mathcal{O}(1)}$. Recently, Hegerfeld and Kratsch (STACS'20) showed that, for some of those problems, the Cut&Count technique can be also applied in the setting of treedepth, and it gives algorithms with running time $2^{\mathcal{O}(d)}\cdot n^{\mathcal{O}(1)}$ and polynomial space usage. However, a number of important problems eluded such a treatment, with the most prominent examples being Hamiltonian Cycle and Longest Path. In this paper we clarify the situation by showing that Hamiltonian Cycle, Hamiltonian Path, Long Cycle, Long Path, and Min Cycle Cover all admit $5^d\cdot n^{\mathcal{O}(1)}$-time and polynomial space algorithms on graphs of treedepth $d$. The algorithms are randomized Monte Carlo with only false negatives.Comment: Presented at WG2020. 20 pages, 2 figure

The number of matchings in random graphs

We study matchings on sparse random graphs by means of the cavity method. We first show how the method reproduces several known results about maximum and perfect matchings in regular and Erdos-Renyi random graphs. Our main new result is the computation of the entropy, i.e. the leading order of the logarithm of the number of solutions, of matchings with a given size. We derive both an algorithm to compute this entropy for an arbitrary graph with a girth that diverges in the large size limit, and an analytic result for the entropy in regular and Erdos-Renyi random graph ensembles.Comment: 17 pages, 6 figures, to be published in Journal of Statistical Mechanic

On the State Complexity of Partial Derivative Automata For Regular Expressions with Intersection

Extended regular expressions (with complement and intersection) are used in many applications due to their succinctness. In particular, regular expressions extended with intersection only (also called semi-extended) can already be exponentially smaller than standard regular expressions or equivalent nondeterministic finite automata (NFA). For practical purposes it is important to study the average behaviour of conversions between these models. In this paper, we focus on the conversion of regular expressions with intersection to nondeterministic finite automata, using partial derivatives and the notion of support. First, we give a tight upper bound of 2O(n) for the worst-case number of states of the resulting partial derivative automaton, where n is the size of the expression. Using the framework of analytic combinatorics, we then establish an upper bound of (1.056 + o(1))n for its asymptotic average-state complexity, which is significantly smaller than the one for the worst case. (c) IFIP International Federation for Information Processing 2016

From Loom to Machine: Tibetan Aprons and the Configuration of Place

In this paper I examine how objects become connected to place in complex and contradictory ways. Over the past ten to fi fteen years, rapid transformations in Chinese manufacturing and transportation networks have signifi cantly altered the production, marketing, and consumption of commodities made in the Tibet Autonomous Region and traded in Kalimpong, India, and Kathmandu, Nepal. In an attempt to connect the ethnographic study of material culture with more macrolevel processes of geoeconomic change, I begin the piece with an examination of the changing production, materials, and styles of a very specifi c commodity, the Tibetan women’s apron. I then explore traders’ narratives about the values of handmade, machine-made, wool, and synthetic commodities, arguing that we ought to look beyond dichotomies of ‘old’ versus ‘new’ or ‘authentic’ versus ‘inauthentic’ objects to show in detail how the attachment of commodities to representations of place fi gures importantly in the contemporary study both of globalization and uneven development. Finally, I suggest that Karl Marx’s notion of dead labor is useful in analyzing the recent move towards the revitalization of Tibetan wool for both the domestic Chinese industry and the global tourist industry

Making subaltern shikaris: histories of the hunted in colonial central India

Academic histories of hunting or shikar in India have almost entirely focused on the sports hunting of British colonists and Indian royalty. This article attempts to balance this elite bias by focusing on the meaning of shikar in the construction of the Gond ‘tribal’ identity in late nineteenth and early twentieth-century colonial central India. Coining the term ‘subaltern shikaris’ to refer to the class of poor, rural hunters, typically ignored in this historiography, the article explores how the British managed to use hunting as a means of state penetration into central India’s forest interior, where they came to regard their Gond forest-dwelling subjects as essentially and eternally primitive hunting tribes. Subaltern shikaris were employed by elite sportsmen and were also paid to hunt in the colonial regime’s vermin eradication programme, which targeted tigers, wolves, bears and other species identified by the state as ‘dangerous beasts’. When offered economic incentives, forest dwellers usually willingly participated in new modes of hunting, even as impact on wildlife rapidly accelerated and became unsustainable. Yet as non-indigenous approaches to nature became normative, there was sometimes also resistance from Gond communities. As overkill accelerated, this led to exclusion of local peoples from natural resources, to their increasing incorporation into dominant political and economic systems, and to the eventual collapse of hunting as a livelihood. All of this raises the question: To what extent were subaltern subjects, like wildlife, ‘the hunted’ in colonial India

Efficient Attribute-Based Signatures for Unbounded Arithmetic Branching Programs

This paper presents the first attribute-based signature (ABS) scheme in which the correspondence between signers and signatures is captured in an arithmetic model of computation. Specifically, we design a fully secure, i.e., adaptively unforgeable and perfectly signer-private ABS scheme for signing policies realizable by arithmetic branching programs (ABP), which are a quite expressive model of arithmetic computations. On a more positive note, the proposed scheme places no bound on the size and input length of the supported signing policy ABP’s, and at the same time, supports the use of an input attribute for an arbitrary number of times inside a signing policy ABP, i.e., the so called unbounded multi-use of attributes. The size of our public parameters is constant with respect to the sizes of the signing attribute vectors and signing policies available in the system. The construction is built in (asymmetric) bilinear groups of prime order, and its unforgeability is derived in the standard model under (asymmetric version of) the well-studied decisional linear (DLIN) assumption coupled with the existence of standard collision resistant hash functions. Due to the use of the arithmetic model as opposed to the boolean one, our ABS scheme not only excels significantly over the existing state-of-the-art constructions in terms of concrete efficiency, but also achieves improved applicability in various practical scenarios. Our principal technical contributions are (a) extending the techniques of Okamoto and Takashima [PKC 2011, PKC 2013], which were originally developed in the context of boolean span programs, to the arithmetic setting; and (b) innovating new ideas to allow unbounded multi-use of attributes inside ABP’s, which themselves are of unbounded size and input length