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In this paper we consider the problem of capturing an intruder in a networked environment. The intruder is defined as a mobile entity that moves arbitrarily fast inside the network and escapes from a team of software agents. The agents have to collaborate and coordinate their moves in order to isolate the intruder. They move asynchronously and they know the network topology they are in is a particular fractal graph, the Sierpiński graph SGn. We first derive lower bounds on the minimum number of agents, number of moves and time steps required to capture the intruder. We then consider two models: one in which agents have a capability, of "seeing" the state of their neighbors; the second one in which the actions of the agents are leaded by a coordinator. One of our goals is to continue a previous study on what is the impact of visibility on complexity: we have found that in this topology the visibility assumption allows us to reach an optimal bound on the number of agents required for the cleaning strategy. On the other hand, the second strategy relies only on local computations but requires an extra agent and a higher (by a constant) complexity in terms of time and number of moves. [ABSTRACT FROM AUTHOR]

A central problem in optical networks is to assign wavelengths to a given set of lightpaths, so that at most g of them that share a physical link get the same wavelength (g is the grooming factor). The switching cost for each wavelength is the number of distinct endpoints of lightpaths of that wavelength, and the goal is to minimize the total switching cost. We prove NP-completeness results for the problem of minimizing the switching costs in path networks. First we prove that the problem is NP-complete in the strong sense, when all demands are either 0 or 1, the routing is single-hop, and the number of wavelengths is unbounded. Next we prove that the problem is NP-complete for any fixed g ≥ 2, and when the number of wavelengths is bounded. These results improve upon existing results regarding the complexity of the traffic grooming problem for ring and path networks. [ABSTRACT FROM AUTHOR]

Graphides cincinnatae (also known as circulant graphs) Cin(L) of n vertices are studied here as link farms in the Web, built automatically by a spammer to promote visibility of a page T. These graphs are k-consecutive, denoted by Cin,k, if each vertex vi is connected to vi + j and vi − j with j = 1,2,...,k. Graphides cirratae are cincinnatae with some irregularities. We discuss how to fight this phenomenon with a set of Web marshals, that is autonomous agents that visit the farm for cutting the links to T. The farm reacts reconstructing the links through majority voting among its pages. We prove upper and lower bounds on the number of marshals, and of link hops, needed to dismantle the farm. We consider both synchronous and asynchronous operations. Regular Keywords: Circulant graph, Web graph, Page-rank, Web spam, Link farm, Autonomous agent, Majority rule. Elegant Keywords: Graphis cincinnata, Graphis cirrata, Curly graph, Web marshal. [ABSTRACT FROM AUTHOR]

In the classical wolf-goat-cabbage puzzle, a ferry boat man must ferry three items across a river using a boat that has room for only one, without leaving two incompatible items on the same bank alone. In this paper we define and study a family of optimization problems called Ferry problems, which may be viewed as generalizations of this familiar puzzle. In all Ferry problems we are given a set of items and a graph with edges connecting items that must not be left together unattended. We present the Ferry Cover problem (FC), where the objective is to determine the minimum required boat size and demonstrate a close connection with Vertex Cover which leads to hardness and approximation results. We also completely solve the problem on trees. Then we focus on a variation of the same problem with the added constraint that only 1 round-trip is allowed (FC1). We present a reduction from MAX-NAE-{3}-SAT which shows that this problem is NP-hard and APX-hard. We also provide an approximation algorithm for trees with a factor asymptotically equal to $\frac{4}{3}$. Finally, we generalize the above problem to define FCm, where at most m round-trips are allowed, and MFTk, which is the problem of minimizing the number of round-trips when the boat capacity is k. We present some preliminary lemmata for both, which provide bounds on the value of the optimal solution, and relate them to FC. [ABSTRACT FROM AUTHOR]

A spreadsheet, especially MS Excel, is probably one of the most popular software applications for personal-computer users and gives us convenient and user-friendly tools for drawing tables. Using spreadsheets, we often wish to draw several vertical and horizontal black lines on selective gridlines to enhance the readability of our spreadsheet. Such situations we frequently encounter are formulated as the Border Drawing Problem (BDP). Given a layout of black line segments, we study how to draw it efficiently from an algorithmic view point, by using a set of border styles and investigate its complexity. (i) We first define a formal model based on MS Excel, under which the drawability and the efficiency of border styles are discussed, and then (ii) show that unfortunately the problem is ${\cal NP}$-hard for the set of the Excel border styles and for any reasonable subset of the styles. Moreover, in order to provide potentially more efficient drawing, (iii) we propose a new compact set of border styles and show a necessary and sufficient condition of its drawability. [ABSTRACT FROM AUTHOR]

Heyawake is one of many recently popular Japanese pencil puzzles. We investigate the computational complexity of the problem of deciding whether a given puzzle instance has a solution or not. We show that Boolean gates can be emulated via Heyawake puzzles, and that it is possible to reduce the Boolean Satisfiability problem to Heyawake. It follows that the problem in question is $\textsf{NP}$-complete. [ABSTRACT FROM AUTHOR]

This paper is devoted to the "Discovery of Slowness." The archetypical perversely awful algorithm bogo-sort, which is sometimes referred to as Monkey-sort, is analyzed with elementary methods. Moreover, practical experiments are performed. [ABSTRACT FROM AUTHOR]

We consider cryptographic and physical zero-knowledge proof schemes for Sudoku, a popular combinatorial puzzle. We discuss methods that allow one party, the prover, to convince another party, the verifier, that the prover has solved a Sudoku puzzle, without revealing the solution to the verifier. The question of interest is how a prover can show: (i) that there is a solution to the given puzzle, and (ii) that he knows the solution, while not giving away any information about the solution to the verifier. In this paper we consider several protocols that achieve these goals. Broadly speaking, the protocols are either cryptographic or physical. By a cryptographic protocol we mean one in the usual model found in the foundations of cryptography literature. In this model, two machines exchange messages, and the security of the protocol relies on computational hardness. By a physical protocol we mean one that is implementable by humans using common objects, and preferably without the aid of computers. In particular, our physical protocols utilize scratch-off cards, similar to those used in lotteries, or even just simple playing cards. The cryptographic protocols are direct and efficient, and do not involve a reduction to other problems. The physical protocols are meant to be understood by "lay-people" and implementable without the use of computers. [ABSTRACT FROM AUTHOR]

In this paper we show a polynomial-time algorithm to find the best rational approximation of a given rational number within a given interval. As a special case, we show how to find the best rational number that after evaluating and rounding exactly matches the input number. In both results, "best" means "having the smallest possible denominator". [ABSTRACT FROM AUTHOR]

In this paper, we consider the question: what is the worst possible page-replacement strategy? Our goal is to devise an online strategy that has the highest possible fraction of misses as compared to the worst offline strategy. We show that there is no deterministic, online page-replacement strategy that is competitive with the worst offline strategy. We give a randomized strategy based on the "most-recently-used" heuristic, and show that this is the worst possible online page-replacement strategy. [ABSTRACT FROM AUTHOR]

The Hydra was a many-headed monster from Greek mythology that would immediately replace a head that was cut off by one or two new heads. It was the second task of Hercules to kill this monster. In an abstract sense, a Hydra can be modeled as a tree where the leaves are the heads, and when a head is cut off some subtrees get duplicated. Different Hydra species differ by which subtress can be duplicated in which multiplicity. Using some deep mathematics, it had been shown that two classes of Hydra species must always die, independent of the order in which heads are cut off. In this paper we identify three properties for a Hydra that are necessary and sufficient to make it immortal or force it to die. We also give a simple combinatorial proof for this classification. Now, if Hercules had known this... [ABSTRACT FROM AUTHOR]

Architectures for optical processors designed to solve bounded instances of NP-Complete problems are suggested. One approach mimics the traveling salesman by traveling beams that simultaneously examine the different possible paths. The other approach uses a pre-processing stage in which O(n2) masks are constructed, each representing a different edge in the graph. The choice and combination of the appropriate (small) subset of these masks yields the solution. The solution is rejected in cases where the combination of these masks totally blocks the light and accepted otherwise. We present detailed designs for basic primitives of the optical processor. We propose designs for solving Hamiltonian path, Traveling Salesman, Clique, Independent Set, Vertex Cover, Partition, 3-SAT, and 3D-matching. [ABSTRACT FROM AUTHOR]

In this paper, we explain how Robert Langdon, a famous Harvard Professor of Religious Symbology, brought us to decipher the Code of the Origins. We first formalize the problem to be solved to understand the Code of the Origins. We call it the Scatter Problem (SP). We then show that the SP cannot be deterministically solved. Next, we propose a randomized algorithm for this problem. The proposed solution is trivially self-stabilizing. We then show how to design a self-stabilizing version of any deterministic solution for the Pattern Formation and the Gathering problems. [ABSTRACT FROM AUTHOR]

We analyse transports between leaves in an edge-weighted tree. We prove under which conditions there exists a transport matching the weights of a given tree. We use this to compute minimum and maximum values for the transport between a given pair of leaves. [ABSTRACT FROM AUTHOR]

A spoonerism is a sentence in some natural language where the swapping of two letters results in a new sentence with a different meaning. In this paper, we give some efficient algorithms for deciding whether a given sentence, made up from words of a given dictionary, is a spoonerism or not. [ABSTRACT FROM AUTHOR]

You are back from that very long, marvelous journey. You have a thousand pictures, but your friends and relatives will stand just a few dozens. Choosing is a painful process, in particular when you cannot decide between the silent vastity of that desert and the idyllic picture of that tranquil, majestic lake. We are going to help. [ABSTRACT FROM AUTHOR]

In this paper we investigate the relations between knitting and computer science. We show that the two disciplines share many concepts. Computer science, in particular algorithm theory, can suggest a lot of powerful tools that can be used both in descriptive and prescriptive ways and that apparently have not yet been used for creative knitting. The obtained results are short (optimal size) recursive descriptions for complex patterns; creation of new complex recursive patterns; and the application of three-valued algebra operations to combine and create a wide variety of new patterns. [ABSTRACT FROM AUTHOR]

We study some combinatorial properties related to the problem of tablature for stringed instruments. First, we describe the problem in a formal way and prove that it is equivalent to a finite state automaton. We define the concepts of distance between two chords and tablature complexity in order to study the problem of tablature in terms of music performance. By using the Schützenberger methodology we are then able to find the generating function counting the number of tablatures having a certain complexity and we can study the average complexity for the tablatures of a music score. [ABSTRACT FROM AUTHOR]

In a Hiroimono puzzle, one must collect a set of stones from a square grid, moving along grid lines, picking up stones as one encounters them, and changing direction only when one picks up a stone. We show that deciding the solvability of such puzzles is NP-complete. [ABSTRACT FROM AUTHOR]

We discuss some new geometric puzzles and the complexity of their extension to arbitrary sizes. For gate puzzles and two-layer puzzles we prove NP-completeness of solving them. Not only the solution of puzzles leads to interesting questions, but also puzzle design gives rise to interesting theoretical questions. This leads to the search for instances of partition that use only integers and are uniquely solvable. We show that instances of polynomial size exist with this property. This result also holds for partition into k subsets with the same sum: We construct instances of n integers with subset sum O(nk + 1), for fixed k. [ABSTRACT FROM AUTHOR]

Graph Drawing is (usually) concerned with the production of readable representations of graphs. In this paper, instead of investigating how to produce "good" drawings, we tackle the opposite problem of producing "bad" drawings. In particular, we study how to construct orthogonal drawings with many bends along the edges and with large area. Our results show surprising contact points, in Graph Drawing, between the computational cost of niceness and the one of ugliness. [ABSTRACT FROM AUTHOR]

Provided that one is willing to use randomness and to tolerate an approximate answer, many computational problems admit ultra-fast algorithms that run in less than linear time in the length of the input. In many interesting cases, even algorithms that run in constant time are known, whose efficiency depends only on the accuracy of the approximation and not on the length of the inputs. Algorithms for graph problems on dense graphs are especially efficient and simple. I will describe an algorithm that estimates the size of the maximum cut in a dense graph, and its specialization to the task of distinguishing bipartite dense graphs from dense graphs that are "far from bipartite." Results "explaining" the simplicity of such algorithms will also be discussed. Some sublinear-time algorithms are also known for graph problems in sparse graphs, but they are typically more elaborate. I will describe a simple but very clever algorithm that approximates the number of connected components of a given graph, and its generalization to the problem of approximating the weight of the minimum spanning tree of a given weighted graph. The algorithm runs in time dependent only on the maximum degree, the required quality of approximation, and the range of weights, but the running time is independent of the number of vertices. [ABSTRACT FROM AUTHOR]

Consider a netscape inhabited by mobile computational entities (e.g., robots, agents, sensors). In the algorithmic literature, these environments are usually assumed to be safe for the entities. Outside of the literature, this is hardly the case: highly harmful objects can operate in the netscape rendering the environment dangerous for the entities. A particular example is the presence of a black hole: a network site (node, host) that disposes of any incoming robot/agent, leaving no observable trace of such a destruction. The reasons why a node becomes a black hole are varied; for example, the presence at a node of a harmful static process (e.g., a virus) that destroys incoming code and messages transforms that node into a black hole; the undetectable crash failure of a host renders that host a black hole; "receive-omission" failures in the communication software of a site makes that site act as a black hole. Indeed, this type of danger is not rare. Clearly the presence of a black hole renders computations in the net dangerous to be performed, and some tasks become impossible to be carried out. We will examine two classic problems for mobile entities, Exploration and Gathering (or Rendezvous), and discuss how they are affected by the presence of a black hole. In particular, we will view them with respect to a new task that, in this context, is even more basic and essential: Black Hole Search, the problem of a team of mobile entities locating the black hole. Obviously, any entity entering the black hole is destroyed; the black hole location problem is solved if at least one agent survives, and all surviving agents know the location of the black hole. Not satisfied with correctness, our focus is on efficiency. The basic cost measures are the number of entities (and of casualties), and the number of moves. [ABSTRACT FROM AUTHOR]